Book Description
Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.
The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.
* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon
NEW IN THIS EDITION
* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems
Customer Reviews:
A new version of a classic book.......2007-02-21
I bought a copy of this new book and I have its old version with Hirsch and Smale as its only authors. Main differences between these books are some new chapters covering chaos and the exercises. Old version has better chapters dealing with linear algebra. I find this new version hard to read and it leaves many details to be filled by the reader. I would say that the new version is still a good choice for a second course in ODE or supplementary text for a graduate course. I gave it four stars.
Excellent Book.......2006-05-05
This is a great introduction to the next stage of differential equations after a first course. Devaney is a master of presenation, and makes everything seem easy. It is not as encyclopedic as some other books on this material, such as Arnold and Perko, but it is easier to read and still covers the most important advanced material.
good, not ideal.......2005-12-08
the two books by hirsch smale, one with devaney, seem like good books, but I am not crazy about either, at least from the few pages one can search online here.
the latter book with devaney just seems a dumbed down version of the earlier book by the two more famous authors. i expected that earlier book to be far better, but found to my regret that the two books actually share almost the same first page, and the main difference noticeable in the early going is that the 2 author work is poorly written, and the 3 author one is not written much better.
it is clearer but seems to be talking down to the reader in an annoying way. so neither is the absolute pleasure to read that the wonderfully written text of arnol'd is, or the classic of hurewicz. i would skip these books and get arnold and hurewicz instead.
New Edition.......2004-02-26
You should be aware that there are two similar books with similar titles by the same authors. The old edition is a hardcover all green book by Hirsch and Smale called:
"Differential Equations, Dynamical Systems and Linear Algebra"
The second with the lorenz attractors in yellow on the cover is by Hirsch, Smale and Devaney and is called:
"Differential Equations, Dynamical Systems and an Introduction to Chaos"
Now, that may be obvious to you, but it is important to note that because those are VERY different books (which I have both of right here). The 'old' one is a more theoretical text that mainly addresses linear systems and is organized more like a math monograph than a contemporary (i.e. with pictures and examples) textbook. It is difficult for most people. The newer version is COMPLETELY different and is written for a more diverse audience. It starts with linear systems but then goes into nonlinear systems and discrete systems. It is somewhat similar in character to Strogatz's Nonlinear Dynamics and Chaos. If you do not have a very strong abstract theoretical type of math background I would not recommend you start learning about differential equations from the "old" edition. You will find it very difficult. If you are used to a general abstract presentation of results you should be fine. For the NEW edition the level is very different. I would guess that courses in multi-variable calc, elementary diff eq, and linear algebra (if you understood them) would be sufficient preparation. Both books are excellent, just be clear on what you are looking for.
Book Description
The study of nonlinear dynamical systems has exploded in the past 25 years, and Robert L. Devaney has made these advanced research developments accessible to undergraduate and graduate mathematics students as well as researchers in other disciplines with the introduction of this widely praised book. In this second edition of his best-selling text, Devaney includes new material on the orbit diagram fro maps of the interval and the Mandelbrot set, as well as striking color photos illustrating both Julia and Mandelbrot sets. This book assumes no prior acquaintance with advanced mathematical topics such as measure theory, topology, and differential geometry, Assuming only a knowledge of calculus, Devaney introduces many of the basic concepts of modern dynamical systems theory and leads the reader to the point of current research in several areas.
Customer Reviews:
Great Introduction to the topic.......2007-03-09
This is a very good book. Actually, Devaney's "First Course in Chaotic Dynamical Systems," is a good accompanying text. Fascinating subject...
Excellent book; unique in its accessibility and coverage of deep results.......2005-09-14
This book is an introduction to dynamical systems defined by iterative maps of continuous functions. It doesn't require much advanced knowledge, but it does require a familiarity and certain level of comfort with proofs. The basic idea of this book is to explore (in the context of iterative maps) the major themes of dynamical systems, which can later be explored in the messier setting of differential equations and continuous-time systems. While this book doesn't discuss differential equations directly, the techniques used here can be transferred (with considerable work and thought) to that setting. Someone wanting an elementary book covering differential equations as dynamical systems might want to check out the excellent multi-volume work by J. Hubbard; the combination of that work with this book would provide the background to tackle the tougher and less-accessible texts dealing with chaotic systems of differential equations.
Although this is a pure math book, the book does mention key applications and motivation behind the material; applied mathematicians will find this book quite useful, not necessarily because of the choice of topics but just because it greatly helps develop ones' intuition. The material is presented in a way that gives the student a sense of the big picture--what the theorems mean, how they fit together. Proofs are rigorous but as easy to follow as I have seen them in this subject.
The choice and order of subjects is also both practical and fun. The book begins with 1-dimensional systems and explores just about everything interesting that happens with them (including Sarkovski's Theorem, one of the most bizarre and surprising mathematical results), before moving into two-dimensions and then dynamics in the complex plane.
The bottom line? This book would be excellent both as a textbook and for self-study. If you're interested in this subject at all, this is a book you will want on your shelf. I know of no other book on the subject that covers such deep material while remaining as accessible.
Good introduction to the beginning student.......2001-08-11
This book gives a quick and elementary introduction to the field of chaotic dynamical systems that could be read by anyone with a background in calculus and linear algebra. The approach taken by the author is very intuitive, lots of diagrams are used to illustrate the major points, and there are many useful exercises throughout the book. It could serve well in an undergraduate mathematics course in dynamical systems, and in a physics undergraduate course in advanced mechanics. The author emphasizes the mathematical aspects of dynamical systems, and readers will be well prepared after finishing it to read more advanced books on dynamical systems.
Chapter 1 introduces one-dimensional dynamics, with the analysis of the quadratic map given particular attention. Called the logistic map in some circles, this very important dynamical system has been the subject of much study, and exhibits generically the properties of chaotic dynamical systems. The author also gives a brief review of some elementary notions in calculus needed for the chapter, making the book even more accessible to a wider readership. The important concept of hyperbolicity is discussed in the context of one-dimensional maps and a good discussion is given on symbolic dynamics. Structural stability, which is really useful only in dynamical systems in higher dimensions, is treated here. The intuition gained in one-dimension is invaluable though before moving on to higher-dimensional examples. Sarkovskii's theorem, which states that a one-dimensional dynamical system with a period three periodic orbit has periodic orbits for all other periods, is proved in detail. In addition, the Schwarzian derivative, so important in complex dynamics, is defined here. The author also gives an introduction to bifurcation theory, which again, is most interesting in high dimensions, and introduces the concept of homoclinicity in this discussion. Maps of the circle and the all-important Morse-Smale diffeomorphisms, are treated in this chapter also. The author introduces the reader briefly to the idea of genericity when discussing Morse-Smale diffeomorphisms. Kneading theory, so important in the mathematical theory of dynamical systems, is introduced here also.
In chapter 2, the author generalizes the results to higher dimensions, and begins with a review of linear algebra and some results from multivariable calculus, such as the implicit function theorem and the contraction mapping theorem. This is followed by a treatment of the dynamics of linear maps in two and three dimensions. Whereas the canonical example of one-dimensional dynamics is represented by the logistic map, in higher-dimensional dynamics this is represented by the Smale horseshoe map. The author carefully constructs this map and details its properties. Then he takes up the hyperbolic toral automorphisms (or Anosov systems as they are called in some books). Both the Smale horseshoe map and the toral automorphisms are excellent, easily understandable examples of higher dimensional dynamics and the associated symbolic dynamics.
The concept of an attractor is also treated in chapter 2 in the context of the solenoid and the Plykin attractor. Both of these are of purely mathematical interest, but by studying them the physicist reader can get a better understanding of what to look for in actual physical examples of attractors (or the more exotic concept of a strange attractor). The author also gives a proof of the stable manifold theorem in dimension two. This is the best part of the book, for this theorem is rarely proved in textbooks on chaotic dynamics, the proof being delegated to the original papers. However, the proof in these papers is extremely difficult to get through, and so the author has given the reader a nice introduction to this important result, even though it is done only in two dimensions. This is followed by a very understandable discussion of Morse-Smale diffeomorphisms. In addition, the author introduces the Hopf bifurcation, of upmost importance in applications, and introduces the Henon map as an application of the results obtained so far.
The last chapter of the book is a brief overview of complex analytic dynamics. Complex dynamical systems are very important from a mathematical point of view, and they have fascinating connections with number theory, cryptography, algebraic geometry, and coding theory. The author reviews some elementary complex analysis and then reintroduces the quadratic maps but this time over the complex plane instead of the real line. The Julia set is introduced, and the reader who has not seen the computer graphical images of this set should peruse the Web for these images, due to their beauty. The geometry of the Julia set and the associated complex polynomial maps are given a fairly detailed treatment by the author in the space provided.
The best starting point........2000-06-25
This book covers almost every aspect of theory of discrete dynamical systems and by far the easiest explains and proofs with useful exercises, anyone with solid calculus and linear algebra background shouldn't have any problem absorbing this material and is highly recommended to whom wants to know about the theory of chaos from the scratch.
The best starting point........2000-06-25
This book covers almost every aspect of theory of discrete dynamical systems and by far the easiest explains and proofs with useful exercises, anyone with solid calculus and linear algebra background shouldn't have any problem absorbing this material and is highly recommended to whom wants to know about the theory of chaos from the scratch.
Book Description
Largely self-contained, this is an introduction to the mathematical structures underlying models of systems whose state changes with time, and which therefore may exhibit "chaotic behavior." The first portion of the book is based on lectures given at the University of London and covers the background to dynamical systems, the fundamental properties of such systems, the local bifurcation theory of flows and diffeomorphisms and the logistic map and area-preserving planar maps. The authors then go on to consider current research in this field such as the perturbation of area-preserving maps of the plane and the cylinder. The text contains many worked examples and exercises, many with hints. It will be a valuable first textbook for senior undergraduate and postgraduate students of mathematics, physics, and engineering.
Customer Reviews:
Excellent Introduction to the Subject.......2001-05-24
covers most important areas of the subject with a clear yet rigorous approach. Advanced text better suited for graduate students in applied math. It promises as a must for anyone serious about the subject
Excellent focus on what is important.......1997-11-29
Dynamical systems is a vast subject to which no single book can provide an adequate introduction, but the authors do an excellent job of focusing on what is important and avoiding the temptation to go off on enticing tangents. Their treatment is clear, and this book is highly recommended for any student seeking a solid foundation for further work.
Average customer rating:
- First Aid to those outside the EE community
- Systems theory done right!
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Introduction to Mathematical Systems Theory : A Behavioral Approach (Texts in Applied Mathematics, Vol. 26)
Jan Willem Polderman , and
Jan C. Willems
Manufacturer: Springer
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ASIN: 0387982663 |
Book Description
This is a book about modelling, analysis and control of linear time- invariant systems. The book uses what is called the behavioral approach towards mathematical modelling. Thus a system is viewed as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. In the first part of the book the structure of the set of trajectories that such dynamical systems generate is analyzed. Conditions are obtained for two systems of differential equations to be equivalent in the sense that they define the same behavior. It is further shown that the trajectories of such linear differential systems can be partitioned in free inputs and bound outputs. In addition the memory structure of the system is analyzed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. An essential feature of using the behavioral approach is that it allows these and similar concepts to be introduced in a representation-free manner. In the third part control problems are considered, more specifically stabilization and pole placement questions. This text is suitable for advanced undergraduate or beginning graduate students in mathematics and engineering. It contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.
Customer Reviews:
First Aid to those outside the EE community.......2006-12-02
The book starts off with an extremely useful modeling term: "Exclusion Law." This term describes a notion that any closed system of physical laws/equations (Newton's, etc.) state what's included (possible) and what's excluded (impossible) from its (a certain set of physical laws/equations) interpretation of reality.
Most of the concepts in this text will be nothing new to those who already have a bachelor of science in electrical engineering. Still, learning from the author's choice of words and his arrangement of materials will provide one with a very effective way of communicating modeling ideas to those outside the EE community or to those who are somehow academically juvenile (for example, speaking with someone who had to suffer a poor signals and systems instructor or with anyone who had to deal with a similar academic situation).
Here's a quote from page 12:
"Now it becomes necessary to consider two cases:"
From page 1:
"We view a mathematical model as an exlcusion law. A mathematical model expresses the OPINION that some things can happen, are possible, while others cannot, are declared impossible. Thus Kepler claims that planetary orbits that do not satisfy his three famous laws are impossible. In particular, he judges nonelliptical orbits as unphysical. ... Economic production functions tell us that certain amounts of raw materials, capital, and labor are needed in order to manufacture a finished product: it prohibits the creation of finished products unless the required resources are available."
And from page 8:
"Dynamical Systems.... The adjective dynamical refers to phenomena with a delayed reaction, phenomena with an aftereffect, with transients, oscillations, and, perhaps, an approach to equilibrium. ...a mathematical model in which the objects of interest are functions of time..."
Systems theory done right!.......2004-04-06
This is an excellent book on mathematical control theory. As opposed to the classical state-space approach, the behavioural theory gives a more fundamental and natural way of looking at physical systems. The book deals with the notions of controllability, observability, stability and feedback in a beautiful mathematical framework. A more appropriate title would be "Systems theory done right"!
Book Description
This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has placed emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about the behavior of these systems. He has included the basic core material that is necessary for higher levels of study and research. Thus, people who do not necessarily have an extensive mathematical background, such as students in engineering, physics, chemistry, and biology, will find this text as useful as students of mathematics.
This new edition contains extensive new material on invariant manifold theory and normal forms (in particular, Hamiltonian normal forms and the role of symmetry). Lagrangian, Hamiltonian, gradient, and reversible dynamical systems are also discussed. Elementary Hamiltonian bifurcations are covered, as well as the basic properties of circle maps. The book contains an extensive bibliography as well as a detailed glossary of terms, making it a comprehensive book on applied nonlinear dynamical systems from a geometrical and analytical point of view.
Customer Reviews:
Great reference or grad school level course text on general nonlinear dynamics.......2007-04-15
This book served as the "hidden basis" for a course in nonlinear dynamics by the late John David Crawford back at the University of Pittsburgh (the overt basis was Glendinning's book, which has proved less appealing as a reference). It's subsequently been useful to me in its treatment of Melnikov's method, and to review ideas in bifurcation theory.
As the other reviewer pointed out, it is weak in the section on symbolic dynamics. In its defense, I only know of one book which treats symbolic dynamics in a way that isn't utterly confusing, so perhaps leaving a lot of it out helps keep the student on track towards what the author is trying to present. Certainly, if he stuck to his theorem heavy style, one could get very lost in symbolic dynamics land. I'll also complain he never mention's Painleve's property. There are probably deep "theorist" reasons I'll never understand for his not mentioning this weird little thing. I hear the full treatment of Painleve's property is pretty complex, but I have always found it very helpful in understanding what integrability really is, in my "seat of the pants" way. I also would have liked more detail on Peixoto's theorem. Sure it's only useful in R2; if you're on the 'applied' side of things (or a student, learning by examining practical examples) -how often will you leave R2-land?
These complaints are minor, and they're probably effectively complaints that the book's author has a different purpose in mind than I would for writing such an introductory text, were I actually qualified to do such a thing. Wiggins writes very clearly, and he writes for physicists rather than mathematicians, and brings an amateur in the subject to a fairly high level of sophistication by the end of the text. The problem sets are also excellent.
Effective overview of a useful subject.......2001-06-10
The subject of dynamical systems has been around for over a century now, having been defined by Henri Poincare in the early 1900s, but having its roots in Hamiltonian and Lagrangian mechanics in the 19th century. In this book ths author has done a fine job of overviewing the subject of dynamical systems, particularly with regards to systems that exhibit chaotic behavior. There are 292 illustrations given in the book, and they effectively assist in the understanding of a sometimes abstract subject.
After a brief introduction to the terminology of dynamical systems in Section 1.1, the author moves on to as study of the Poincare map in the next section. Recognizing that the construction of the Poincare map is really an art rather than a science, the author gives several examples of the Poincare map and discusses in detail the properties of each. Structural stability, genericity, transversality are defined, and, as preparation for the material later on, the Poincare map of the damped, forced Duffing oscillator is constructed. The later system serves as the standard example for dynamical systems exhibiting chaotic behavior.
The simplification of dynamical systems by means of normal forms is the subject of the next part, which gives a thorough discussion of center manifolds. Unfortunately, the center manifold theorem is not proved, but references to the proof are given.
Local bifurcation theory is studied in the next part, with bifurcations of fixed points of vector fields and maps given equal emphasis. The author defines rigorously what it means to bifurcate from a fixed point, and gives a classification scheme in terms of eigenvalues of the linearized map about the fixed point. Most importantly, the author cautions the reader in that dynamical systems having time-dependent parameters and passing through bifurcation values can exhibit behavior that is dramatically different from systems with constant parameters. He does give an interesting example that illustrates this, but does not go into the singular perturbation theory needed for an effective analysis of such systems.
An introduction to global bifurcations and chaos is given in the next part, which starts off with a detailed construction of the Smale horseshoe map. Symbolic dynamics, so important in the construction of the actual proof of chaotic behavior is only outlined though, with proofs of the important results delegated to the references. The Conley-Moser conditions are discussed also, with the treatment of sector bundles being the best one I have seen in the literature. The theory is illustrated nicely for the case of two-dimensional maps with homoclinic points. The all-important Melnikov method for proving the existence of transverse homoclinic orbits to hyperbolic periodic orbits is discussed and is by far one of the most detailed I have seen in the literature. The author employs many useful diagrams to give the reader a better intuition behind what is going on. He employs also the pips and lobes terminology of Easton to study the geometry of the homoclinic tangles. Homoclinic bifurcation theory is also treated in great detail. This is followed by an overview of the properties of orbits homoclinic to hyperbolic fixed points. A brief introduction to Lyapunov exponents and strange attractors is also given.
This book has served well as a reference book and should be useful to students and other individuals who are interested in going into this area. It is a subject that has found innumerable applications, and it will continue to grow as more tools and better computational facilities are developed to study the properties of dynamical systems.
Book Description
This book gives an introduction into the ideas of dynamical systems. Its main emphasis is on the types of behavior which nonlinear systems of differential equations can exhibit.
It is divided into two parts which can be read in either order: the first part treats the aspects coming from systems of nonlinear ordinary differential equations, and the second part is comprised of those aspects dealing with iteration of a function.
For professionals with a strong mathematics background.
Average customer rating:
- Horrible
- Applause for Martelli's Chaos !
- Applause for Martelli's Chaos !
- Text for Mathematicians and Scientists.
|
Introduction to Discrete Dynamical Systems and Chaos (Wiley-Interscience Series in Discrete Mathematics and Optimization)
Mario Martelli
Manufacturer: Wiley-Interscience
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ASIN: 0471319759 |
Book Description
A timely, accessible introduction to the mathematics of chaos.
The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized.
Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks.
An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60ew, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
Customer Reviews:
Horrible.......2003-03-21
It is soo hard to understand the theorems in this book it's ridiculous. You will only like this book if you already know the material well...e.i. it's useless for you if you want to learn something. My whole class is having trouble with this book. I'm writing this review cuz i'm so angry at this book.
Applause for Martelli's Chaos !.......2000-10-18
This text is about chaos and discrete dynamical systems, but the organization, presentation and discourse of these topics in this wonderful edition are anything but chaotic. The writing and context of the ideas laid out bristles with personality and clear focus for presenting the student with adequate examples and detail. This book serves as a superb introduction to the area, and is rich with a wide variety of situations and problems that will motivate the novice and still challenge those with background. I signed on to teach an introductory course on Chaos at New Mexico Highlands University (I'm am one of three math faculty at this institution). I spent considerable time searching for a text that adequately addressed chaos and dynamical systems, that was challenging and yet personable and reader friendly. We have a wide disparity of math students at NMHU, particularly with regard to background, ability and vocational aspirations. It was important to use a text, I felt, that did not sacrifice detail, but at the same time did not pre-suppose overly technical sophistication. Most of the texts that I sampled, were quite terse, demanding or pedagogically constipated. When I came across MArtelli's text I was struck by the absence of these defects and then by the simple structure and sequence of topics that patiently build and reinforce concepts. The author's enthusiasm for the material comes through clearly and reaction from students I test-sampled echoed this feeling. In fact, both students have decided to enroll in my spring course - I believe their postiive response to this text was more than a contributing factor. In exchange for their time, I promised I would relay encouragement for all who are considering similar course offerings and a companion text that supports and reinforces the excitement of this area of mathematics. This book is a great resource. Bravo, Mario !!
Applause for Martelli's Chaos !.......2000-10-18
This text is about chaos and discrete dynamical systems, but the organization, presentation and discourse of these topics in this wonderful edition are anything but chaotic. The writing and context of the ideas laid out bristles with personality and clear focus for presenting the student with adequate examples and detail. This book serves as a superb introduction to the area, and is rich with a wide variety of situations and problems that will motivate the novice and still challenge those with background. I signed on to teach an introductory course on Chaos at New Mexico Highlands University (I'm am one of three math faculty at this institution). I spent considerable time searching for a text that adequately addressed chaos and dynamical systems, that was challenging and yet personable and reader friendly. We have a wide disparity of math students at NMHU, particularly with regard to background, ability and vocational aspirations. It was important to use a text, I felt, that did not sacrifice detail, but at the same time did not pre-suppose overly technical sophistication. Most of the texts that I sampled, were quite terse, demanding or pedagogically constipated. When I came across MArtelli's text I was struck by the absence of these defects and then by the simple structure and sequence of topics that patiently build and reinforce concepts. The author's enthusiasm for the material comes through clearly and reaction from students I test-sampled echoed this feeling. In fact, both students have decided to enroll in my spring course - I believe their postiive response to this text was more than a contributing factor. In exchange for their time, I promised I would relay encouragement for all who are considering similar course offerings and a companion text that supports and reinforces the excitement of this area of mathematics. This book is a great resource. Bravo, Mario !!
Text for Mathematicians and Scientists........2000-10-15
The Introduction to Discrete Dynamical Systems and Chaos is an excellent text for those who just start sturying descrete dynamical systems and for those who already have some knowledge in the field. The book can be used as a textbook or as a guide for individual studies. In the first case the instructors will find a set of carefully chosen problems at the end of each chapter and several interesting projects for the students. While the first part of the book can be understood by a person without extensive mathematical background, the second part deals with topics such as nonlinear dynamical systems and chaotic behavior using Banach contraction principle, fractal dimension, etc.
To illustrate the use of dynamical systems the book also describes few very common models: blood-sell population, predator-prey, Lorenz Model, and neural networks.
The appendix on Mathematica and Dynamical Systems can be used by students to work on the sample projects offered by the author or by scientists to model and investigate the behavior of variety of dynamical system.
Book Description
This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.
Customer Reviews:
An interesting approach.......2007-05-18
Firstly, this is one of those rare technical books which one can thoroughly enjoy. It can be read at a number of levels and rewards any effort put into understanding the concepts and the mathematics. One needs decent calculus, basic set theory and a bit of topology to wade through the maths. The text and diagrams are clear and unambiguous. The fonts and layout are well chosen for easy reading, always an important consideration for technical books. As this is a text book for a course in elementary chaos theory, the authors write out the proofs fully, in an almost bullet point fashion which makes it very easy to follow the argumentation. I like this style very much.
What I don't like is the lack of solutions (preferably worked solutions) to the excellent exercises at the end of each topic. This is one of my major bugbears about textbooks. Without worked solutions one simply cannot get the feedback required for a full understanding of the subject. Not everyone who buys the book will be attending classes and they will never know if they are on track or not. To make me even crankier, the authors will provide worked solutions to "bona fide" teachers who contact them. How about letting teachers, bona fide or otherwise, write their own exercises instead of taking the easy way out, and letting students learn using the well accepted techniques of feedback and reinforcement.
A star is lost! Hufff!
You Don't Need a Math Degree to Understand this.......2004-01-03
Chaos is such a visually stunning field of study, since you invariably run into those computer generated figures of Julia sets or random fractal landscapes or cloud formations.
But can we get a rigorous, first principles explanation that is broadly accessible to undergraduates with good, but not advanced math preparation? Well, you might consider this recent book. The authors have gone to some length to explain events without appealing to more than simple calculus.
Nothing flashy. But you can obtain a good understanding of fractal dimensions, self iterating systems (like a Sierpinski gasket) and noise.
Average customer rating:
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Dynamical Systems
PIERRE TU
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback
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Chaos & Systems
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ASIN: 0387576614 |
Book Description
This book - perhaps the only of its kind - gives a comprehensive account of Dynamical Systems in a plain non-technical language which is as rigorous as it can be made at this introductory level. Starting from the first steps of differential equations, on the assumption that readers only have a modest mathematical background, it quickly takes them to nonlinear dynamical systems, linearization theory, limit cycles, Gradient, Lagrangean and Hamiltonian dynamical systems. Apart from a new chapter on Floquet theory, Centre Manifold theorems and Liapunov-Schmidt reduction, this second edition also includes new materials, additional examples, illustrations and applications: almost every chapter has been re-written and enlarged to keep up with rapid advances in this field.
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Chaos and Chance: An Introduction to Stochastic Aspects of Dynamics
Arno Berger
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Paperback
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Calculus
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Differential Equations
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Differential Equations
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ASIN: 3110169908 |
Book Description
With emphasis on stochastic aspects of deterministic systems this short book introduces the reader to the basic facts and some special topics of applied ergodic theory. It addresses advanced undergraduate and graduate students from various disciplines, i.e. mathematicians, physicists, electrical and mechanical engineers. Based upon a sound (but non-technical) mathematical introduction, a number of typical examples from applications (mostly from mechanics) are thoroughly discussed. By studying both probabilistic and deterministic features of dynamical systems the reader will develop what might be considered a unified view on chaos and chance as two sides of the same thing.
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