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
This introduction to dynamical systems theory treats both discrete dynamical systems and continuous systems. Driven by numerous examples from a broad range of disciplines and requiring only knowledge of ordinary differential equations, the text emphasizes applications and simulation utilizing MATLAB®, Simulink®, and the Symbolic Math toolbox.
Beginning with a tutorial guide to MATLAB®, the text thereafter is divided into two main areas. In Part I, both real and complex discrete dynamical systems are considered, with examples presented from population dynamics, nonlinear optics, and materials science. Part II includes examples from mechanical systems, chemical kinetics, electric circuits, economics, population dynamics, epidemiology, and neural networks. Common themes such as bifurcation, bistability, chaos, fractals, instability, multistability, periodicity, and quasiperiodicity run through several chapters. Chaos control and multifractal theories are also included along with an example of chaos synchronization. Some material deals with cutting-edge published research articles and provides a useful resource for open problems in nonlinear dynamical systems.
Approximately 330 illustrations, over 300 examples, and exercises with solutions play a key role in the presentation. Over 60 MATLAB® program files and Simulink® model files are listed throughout the text; these files may also be downloaded from the Internet at: http://www.mathworks.com/matlabcentral/fileexchange/. Additional applications and further links of interest are also available at the author's website.
The hands-on approach of
Dynamical Systems with Applications using MATLAB® engages a wide audience of senior undergraduate and graduate students, applied mathematicians, engineers, and working scientists in various areas of the natural sciences.
Reviews of the author’s published book
Dynamical Systems with Applications using Maple®:
"The text treats a remarkable spectrum of topics…and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple®." – U.K. Nonlinear News
"…will provide a solid basis for both research and education in nonlinear dynamical systems." – The Maple Reporter
Book Description
From the reviews: "This book is concerned with the application of methods from dynamical systems and bifurcation theories to the study of nonlinear oscillations. Chapter 1 provides a review of basic results in the theory of dynamical systems, covering both ordinary differential equations and discrete mappings. Chapter 2 presents 4 examples from nonlinear oscillations. Chapter 3 contains a discussion of the methods of local bifurcation theory for flows and maps, including center manifolds and normal forms. Chapter 4 develops analytical methods of averaging and perturbation theory. Close analysis of geometrically defined two-dimensional maps with complicated invariant sets is discussed in chapter 5. Chapter 6 covers global homoclinic and heteroclinic bifurcations. The final chapter shows how the global bifurcations reappear in degenerate local bifurcations and ends with several more models of physical problems which display these behaviors." #Book Review - Engineering Societies Library, New York#1 "An attempt to make research tools concerning `strange attractors' developed in the last 20 years available to applied scientists and to make clear to research mathematicians the needs in applied works. Emphasis on geometric and topological solutions of differential equations. Applications mainly drawn from nonlinear oscillations." #American Mathematical Monthly#2
Customer Reviews:
Will never collect dust...........2001-06-03
This book has been a continuing source of information and guidance for 18 years now. Students and researchers in many different fields have used this book due to its breadth and detail of coverage. The book does require a fairly advanced mathematical background, but the authors do include a glossary for the reader lacking this.
Chapter one is an overview of differential equations and dynamical systems. All the concepts needed for a study of such systems are discussed in great detail and also very informally, stressing instead the understanding of the concepts, and not merely their definition. Some of the proofs of the main results, such as the Hartman-Grobman and the stable manifold theorems, are omitted however.
This is followed in Chapter 2 by a very intuitive discussion of the van der Pols equation, Duffings equation, the Lorenz equations, and the bouncing ball. Numerical calculations are effectively employed to illustrate some of the main properties of the systems modeled by these equations.
A taste of bifurcation theory follows in Chapter 3. Center manifolds are defined and many examples are given, but the proof of the center manifold theorem is omitted unfortunately. Normal forms and Hopf bifurcations are treated in detail.
Averaging methods are discussed in Chapter 4, with part of the averaging theorem proved using a version of Gronwall's lemma. Several interesting examples of averaging are given, along with a discussion of to what extent the bifurcation properties of the averaged equations carry over to the original equations. Most importantly, this chapter discusses the Melnikov function, so very important in the study of small perturbations of dynamical systems with a hyperbolic fixed point. A full proof that simple zeros of the Melnikov function imply the transversal intersection of the stable and unstable manifolds is given.
Chapter 5 moves on to results of a more purely mathematical nature, where symbolic dynamics and the Smale horseshoe map are discussed. The proofs of the stable manifold theorem and the Palis lambda lemma are, however, omitted. Markov partitions and the shadowing lemma are discussed also but the latter is not proven. The authors do however give a proof of the Smale-Birkhoff homoclinic theorem. A purely mathematical overview of attractors is given along with measure-theoretic (ergodic) properties of dynamical systems.
The (local) bifurcation theory of Chapter 3 is extended to global bifurcations in the next chapter. A very detailed discussion of rotation numbers is given but the KAM theory is only briefly mentioned. The main emphasis is on 1-dimensional maps, the Lorentz system, and Silnikov theory. The authors give a very detailed treatment of wild hyperbolic sets.
The book ends with a discussion of bifurcations from equilibrium points that have multiple degeneracies. The discussion is more motivated from a physical standpont than the last few chapters. But some interesting mathematical constructions are employed, namely the role of k-jets, which have fascinating connections with algebraic goemetry, via the "blowing-up" techniques.
The concepts in the book have proven to have enduring value in the study of dynamical systems, and this book will no doubt continue to serve students and researchers in the years to come.
Background.......2001-01-11
Guckenheimer is one of my favourite book in nonlinear science. Another absolute reference. This books deserved to be milestone in nonlinear dynamics.
Changed the Nature of Science As We Know It........2000-01-26
This book has clearly withstood the test of time in over 15 years of continuous publication. On my bookcase, it stands among my most treasured and well-worn classics of fluid mechanics and differential equations--Hirsch and Smale, Birkhoff and Rota, Chandrasekhar, Bachelor, Lamb, Landau and Lifschitz... It changed many of the unquestioned assumptions of many fields besides my own. It redefined the terms of many scientific debates. And, it changed my life.
I obtained Guckenheimer and Holmes' classic when it first came out in 1983. It was so clear, concise and intellectually engaging that it inspired me to wonder whether the system of equations I was studying for my Ph.D. research at the time--the governing equations of thermal convection at infinite Prandtl number (which govern plate tectonics in the earth's mantle)--might have a chaotic solution. Guckenheimer and Holmes outlined a clear methodology to find out the answer.
My advisor at the University of Chicago thought not. Only steady solutions could be admitted in the absence of external forcing due to the lack of momentum transfer--this belief was widely held at the time, despite certain oscillatory solutions found by Fritz Busse (then at UCLA) and chaotic solutions found in certain limiting cases by Andrew Fowler at Oxford.
In despair, I left my studies at Chicago to work as a Unix sysadmin at my undergraduate alma mater --Cornell, where (unbeknownst to me when I took the job) John Guckenheimer had just relocated from UCSC. Delighted to find him there, I sat in on his courses. Later, with his help, I wrote a proposal to NASA to support the completion of my thesis--with him and Donald Turcotte serving as my advisors.
The 3-year fellowship was approved, and during this time I demonstrated and published that thermal convection at infinite Prandtl number--a condition that pervades many planetary interiors including our own--is indeed chaotic in the absence of external forcing.
Prior to this, planetary convection codes primarily looked for steady state solutions. Since, numerical analysts in the field have upgraded to time-dependent models. The source of chaos at infinite Prandtle number I identified--the heat advection term--is now widely accepted as the source of what is now called "Thermal Turbulence" in planetary interiors.
The defense at Chicago was quite an event. Since my new advisors were flown in from Ithaca, you might say my thesis--The Nonlinear Dynamics of Thermal Convection at Infinite Prandtl Number--passed with flying colors. Someone at Chicago might disagree, but his opinion is irrelevant.
Demonstrating the many possible solutions to a single set of equations and showing how the choice of solution depends very sensitively on the rather poorly-constrained initial conditions of the earth--does render mantle modeling itself rather superfluous and indeed, scientifically suspect. However, many important professors who stayed in the field nonetheless continue to run their time-dependent mantle convection codes, and never cease to wonder at the fact that they all get different results. It's rather amusing, really.
When all that too has passed away, the truths so beautifully put forth in Guckenheimer and Holmes will remain. Like I said, it's a classic. Furthermore, being number 42 in its series, it's got to be the answer to the ultimate question of life, the universe and everything. Was for me, anyway.
Basic and clasic.......1999-08-22
For the moment it is "the" book on Dynamical Systems, through the world. Its first chapter is a good introduction on the mathematics needed to aboard the subject. The second introduces chaos, and the rest is for a good understanding of the newest and prolific science.
Book Description
This book provides a self-contained comprehensive exposition of the theory of dynamical systems. The book begins with a discussion of several elementary but crucial examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate and up.
Customer Reviews:
Great, advanced intro to dynamical systems.......2003-12-20
This is really one of the very best books on dynamical systems available today. Nearly every topic in modern dynamical systems is treated in detail. The authors have provided many important comments and historical notes on the material presented in the main text. The writing is clear and the many topics discussed are given appropriate motivation and background.
There are only two potential drawbacks. First, the prerequisites for this book are quite high. The reader should be familiar with real and functional analysis, differential geometry, topology, and measure theory, for starters. Fortunately a well-organized appendix collects the key results of each of the branches of math for the reader's reference. Second, many dynamical systems of interest to applied mathematicians, scientists, and engineers arise from differential equations. This book does not discuss in much detail the connection between ODEs and continuous dynamical systems. Other books (e.g. Perko) treat this connection more thoroughly.
For completeness, clarity, and rigor, Katok and Hasselblatt is without equal. If you work in dynamical systems, you should definitely have this excellent text on your bookshelf. Highly recommended.
Great book with lots of detail.......2001-05-17
This book is a comprehensive overview of modern dynamical systems that covers the major areas. The authors begin with an overview of the main areas of dynamics: ergodic theory, where the emphasis is on measure and information theory; topological dynamics, where the phase space is a topological space and the "flows" are continuous transformations on these spaces; differentiable dynamics where the phase space is a smooth manifold and the flows are one-parameter groups of diffeomorphisms; and Hamiltonian dynamics, which is the most physical and generalizes classical mechanics. Noticeably missing in the list of references for individuals contributing to these areas are Churchill, Pecelli, and Rod, who have done interesting work in the area of both topological and Hamiltonian mechanics. No doubt size and time constraints forced the authors to make major omissions in an already sizable book.
Some elementary examples of dynamical systems are given in the first chapter, including definitions of the more important concepts such as topological transitivity and gradient flows. The authors are careful to distinguish between topologically mixing and topological transitivity. This (subtle) difference is sometimes not clear in other books. Symbolic dynamics, so important in the study of dynamical systems, is also treated in detail.
The classification of dynamical systems is begun in Chapter 2, with equivalence under conjugacy and semi-conjugacy defined and characterized. The very important Smale horseshoe map and the construction of Markov partitions are discussed. The authors are careful to distinguish the orbit structure of flows from the case in discrete-time systems.
Chapter 3 moves on to the characterization of the asymptotic behavior of smooth dynamical systems. This is done with a detailed introduction to the zeta-function and topological entropy. In symbolic dynamics, the topological entropy is known to be uncomputable for some dynamical systems (such as cellular automata), but this is not discussed here. The discussion of the algebraic entropy of the fundamental group is particularly illuminating.
Measure and ergodic theory are introduced in the following chapter. Detailed proofs are given of most of the results, and it is good to see that the authors have chosen to include a discussion of Hamiltonian systems, so important to physical applications.
The existence of invariant measures for smooth dynamical systems follows in the next chapter with a good introduction to Lagrangian mechanics.
Part 2 of the book is a rigorous overview of hyperbolicity with a very insightful discussion of stable and unstable manifolds. Homoclinicity and the horseshoe map are also discussed, and even though these constructions are not useful in practical applications, an in-depth understanding of them is important for gaining insight as to the behavior of chaotic dynamical systems. Also, a very good discussion of Morse theory is given in this part in the context of the variational theory of dynamics.
The third part of the book covers the important area of low dimensional dynamics. The authors motivate the subject well, explaining the need for using low dimensional dynamics to gain an intuition in higher dimensions. The examples given are helpful to those who might be interested in the quantization of dynamical systems, as the number-theoretic constructions employed by the author are similar to those used in "quantum chaos" studies. Knot theorists will appreciate the discussion on kneading theory.
The authors return to the subject of hyperbolic dynamical systems in the last part of the book. The discussion is very rigorous and very well-written, especially the sections on shadowing and equilibrium states. The shadowing results have been misused in the literature, with many false statements about their applicability. The shadowing theorem is proved along with the structural stability theorem.
The authors give a supplement to the book on Pesin theory. The details of Pesin theory are usually time-consuming to get through, but the authors do a good job of explaining the main ideas. The multiplicative ergodic theorem is proved, and this is nice since the proof in the literature is difficult.
Excellent rigorous introduction to chaotic dynamical system.......1997-04-17
This remarkable book is by far the best rigorous introduction to many facets of the modern theory of (chaotic) dynamical systems. It introduces and rigorously develops the central concepts and methods in dynamical systems in a hands-on and highly insightful fashion. The authors are world experts in smooth dynamical systems and have played a major role in the development of the modern theory and this shows througout the book.
The book starts with a comprehensive discussion of a series of elementary but fundamental examples. These examples are used to formulate the general program of the study of asymptotic properties as
well as to introduce the principal notions (differentiable and topological equivalence, moduli, asymptotic orbit growth, entropies,
ergodicity, etc.) and, in a simplified way, a number of important methods (fixed point methods, coding, KAM-type Newton method, local normal forms, etc.). This chapter alone is worth the price of the
book.
The main theme of the second part is the interplay between local analysis near individual (e.g., periodic) orbits and the global complexity of the orbit structure. This is achieved by exploring
hyperbolicity, transversality, global topological invariants, and variational methods. The methods include study of stable and unstable manifolds, bifurcations, index and degree, and construction of orbits as minima and minimaxes of action functionals.
In the third and fourth part the general program is carried out for low-dimensional and hyperbolic dynamical systems which are particularly amenable to such analysis. In addition these systems have interesting particular properties. For hyperbolic systems there are structural stability, theory of equilibrium (Gibbs) measures, and asymptotic
distribution of periodic orbits, in low-dimensional dynamical systems classical Poincare-Denjoy theory, and Poincare-Bendixson theories are presented as well as more recent developments, including the theory of twist maps, interval exchange transformations and noninvertible interval maps.
This book should be on the desk (not bookshelf!) of any serious student of dynamical systems or any mathematically sophisticated scientist or engineer interested in using tools and paradigms of dynamical systems to model or study nonlinear systems.
Excellent rigorous introduction to chaotic dynamical systems.......1997-04-17
This remarkable book is by far the best rigorous introduction to many facets of the modern theory of (chaotic) dynamical systems. It introduces and rigorously develops the central concepts and methods in dynamical systems in a hands-on and highly insightful fashion. The authors are world experts in smooth dynamical systems and have played a major role in the development of the modern theory and this shows througout the book.
The book starts with a comprehensive discussion of a series of elementary but fundamental examples. These examples are used to formulate the general program of the study of asymptotic properties as
well as to introduce the principal notions (differentiable and topological equivalence, moduli, asymptotic orbit growth, entropies,
ergodicity, etc.) and, in a simplified way, a number of important methods (fixed point methods, coding, KAM-type Newton method, local normal forms, etc.). This chapter alone is worth the price of the
book.
The main theme of the second part is the interplay between local analysis near individual (e.g., periodic) orbits and the global complexity of the orbit structure. This is achieved by exploring
hyperbolicity, transversality, global topological invariants, and variational methods. The methods include study of stable and unstable manifolds, bifurcations, index and degree, and construction of orbits as minima and minimaxes of action functionals.
In the third and fourth part the general program is carried out for low-dimensional and hyperbolic dynamical systems which are particularly amenable to such analysis. In addition these systems have interesting particular properties. For hyperbolic systems there are structural stability, theory of equilibrium (Gibbs) measures, and asymptotic
distribution of periodic orbits, in low-dimensional dynamical systems classical Poincare-Denjoy theory, and Poincare-Bendixson theories are presented as well as more recent developments, including the theory of twist maps, interval exchange transformations and noninvertible interval maps.
This book should be on the desk (not bookshelf!) of any serious student of dynamical systems or any mathematically sophisticated scientist or engineer interested in using tools and paradigms of dynamical systems to model or study nonlinear systems.
Book Description
"Dynamical Systems with Applications using MAPLE" covers standard material for an introduction to dynamical systems theory. The text begins with a tutorial guide to MAPLE and thereafter is divided into two main areas: continuous systems using ordinary differential equations and discrete dynamical systems. In the first part of the text, differential equations are used to model examples taken from various disciplines, including mechanical systems, chemical kinetics, electric circuits, interacting species, and economics. In the second half, both real and complex discrete dynamical systems are considered and examples are taken from economics, population dynamics, nonlinear optics, and materials science.
Approximately 200 illustrations, over 250 examples, and exercises with solutions play a key role in the presentation. The book has a hands-on approach, using MAPLE as a tool throughout.Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters. Some chapters deal with recently published research articles and provide a useful resource for open problems in nonlinear dynamical systems.
The text is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering.
Customer Reviews:
Maple a powerfull tool.......2007-10-08
This is an excellent book. It helps the beginners of "Dynamical Systems" to understand this branch of Mathematical Physics using Maple. It is very useful for undergraduate students as well as for teachers.
More information.......2003-09-30
Thought I'd give a more in depth review than the others here.
Most advanced math textbooks contain one or two chapters that turn me off. I must say that every chapter in this book had useful information or very good applications.
The opening chapter is a brief introduction to Maple V (some Maple 8 commands are posted on the books website). Note that Maple 9 is now out and no doubt Maple X will soon follow.
Chapters 1-7 cover planar systems in some detail, vectorfield in DEplot is a real winner here. Chapters 8 and 9 cover 3D and nonautonomous systems - the poincare command in Maple is a real time saver.
Chapters 10-12 cover a lot of research results on limit cycles - the most lucid I have seen in any textbook.
The remaining half of the book concentrates on both real and complex discrete systems. There are the usual cobweb diagrams, bifurcation diagrams and Mandelbrot set. Where this book comes into its own, however, is in Chapters 16-20.
Lasers and nonlinear optics are investigated using complex iterative maps. Fractals and even multifractals are discussed in some detail. The book ends with a chapter dedicated to chaos control.
Overall, the book is concise with pertinent examples and applications. It is not dogged down with math notation, theorems and proofs.
Strogatz, Perko and Allgood are good books to practice more Maple programing techniques.
This is great book.......2003-08-05
This is only book I find with program files that work right away. Graphics in Maple is excelent for chaotic system and algebra very powerful. I like to rotate figures in 3D and use animation. I learn more about optics, it nice to see complex numbers used in applications. Lots of other applications also.
Book is best for students who want to get programs working quickly. There is a website with working programs. You should also look at Maple Application website for many many examples.
I recomend book to everyone.
very nice introduction to dynamical systems.......2002-02-08
This book is a very nice introduction to the theory of dynamical
systems. It covers all aspects and even more than usually thaught
in a class on dynamical systems. Especially, I like to see
many examples for various applications. These examples and the
Maple programs make it well suitable for students to learn
on dynamical systems by themself.
The MAPLE programs and web pages make this book unique........2001-08-04
A great book. Great web pages and short, easy to copy and edit
Maple programs. Lots of material not covered in other books on this topic. Maple is my favorite package. The others are not
as user friendly. I felt I must write again since amazon have been showing excerpts from book. What a geat idea. Chapters in this book that interested me were fractals, multifractals and
optics. Authors web-site is given on back cover of book. Enjoy!
Book Description
This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2. Equilibrium and long run stability of a dynamical system in which the law of motion is subject to random perturbations is the central theme of Chapters 3-5. A unified account of relatively recent results, exploiting splitting and contractions, that have found applications in many contexts is presented in detail. Chapter 6 explains how a random dynamical system may emerge from a class of dynamic programming problems. With examples and exercises, readers are guided from basic theory to the frontier of applied mathematical research.
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.
Customer Reviews:
Nice begginers text.......2001-07-04
This text is a great begginners guide to chaotic systems, it provides very clear explanations and proofs as well as some examples to help you along.
Excellent book. Explains concepts clearly........1998-05-22
I went from knowing absolutlely nothing about dynamical systems to being able to look at a point on the Mandelbrot Set and visualize what the corresponding Julia Set looks like. Ever wonder why weather cannot be predicted accurately?? Read this book...
Book Description
In this book, methodology of dynamical systems theory is applied to investigate the physics of the large-scale ocean circulation. Topics include the dynamics of western boundary currents such as the Gulf Stream in the Atlantic Ocean and the Kurosio in the Pacific Ocean, the stability of the thermohaline circulation, and the El Niño/Southern Oscillation phenomenon in the Tropical Pacific. The book also deals with the numerical methods to apply bifurcation analysis on large-dimensional dynamical systems, with tens of thousands (or more) degrees of freedom, which arise through discretization of ocean and climate models. The novel approach to understand the phenomena of climate variability is through a systematic analysis of the solution structure of a hierarchy of models using these techniques. In this way, a connection between the results of the different models within the hierarchy can be established. Mechanistic description of the physics of the results is provided and, where possible, links with results of state-of-the-art ocean (and climate) models and observations are sought. The reader is expected to have a background in basic fluid dynamics and applied mathematics, although the level of the text sometimes is quite introductory. Each of the chapters is rather self-contained and many details of derivations are provided. Exercises presented at the end of each chapter make it a perfect graduate-level text.
This book is aimed at graduate students and researchers in meteorology, oceanography and related fields who are interested in tackling fundamental problems in dynamical oceanography and climate dynamics.
Book Description
Several distinctive aspects make Dynamical Systems unique, including: · treating the subject from a mathematical perspective with the proofs of most of the results included · providing a careful review of background materials · introducing ideas through examples and at a level accessible to a beginning graduate student · focusing on multidimensional systems of real variables The book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.
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- Encyclopedia of Physics
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- Essentials of Physics
- Exercise Physiology: Theory and Application to Fitness and Performance
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General
| Science
| Subjects
| Books
Ordinary Differential Equations
A First Course in Partial Differential Equations: with Complex Variables and Transform Methods (Dover Books on Mathematics)
An Introduction to Chaotic Dynamical Systems, 2nd Edition
Applied Linear Algebra
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering
