The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.
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"I highly recommend this book for an advanced undergraduate course in dynamical systems." Mathematical Reviews
Book Description
The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. Its concepts, methods and paradigms have greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This elegant introduction to the subject combines mathematical rigor with copious examples of important applications, covering topics ranging from Newtonian mechanics to coding theory. It will be a valuable first textbook for senior undergraduate and beginning graduate students of mathematics, physics, and engineering.
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5 of 10 people found the following review helpful:
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A Bit Heavy For Me,
By The Dabbler (Boulder, CO, USA) - See all my reviews
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This review is from: A First Course in Dynamics: with a Panorama of Recent Developments (Paperback)
This book has been very challenging for me. I'm not a mathematician (except in my dreams), and this book is heavy with abstract theory. One of the biggest challenges is that the book uses symbology not familiar to me, and there is no glossary of symbols (which would be VERY useful).
I would be interested in what others with a more mathematical background think about the book -- am I wasting my time trying to slog through it? For someone just trying to get a feel for nonlinear dynamics and chaos, I strongly recommend Steven Strogatz's book "Nonlinear Dynamics And Chaos".
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This chapter is a prelude to this book. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Intermediate-Value Theorem, Implicit-Function Theorem, Proof Let, Shadowing Theorem, Inverse-Function Theorem, New York, Anosov Closing Lemma, Cambridge University Press, Shadowing Lemma, American Mathematical Society, Hyperbolic Fixed-Point Theorem, Leonardo of Pisa, Annals of Mathematics, Mean-Value Theorem, Proof Suppose, Proof Take, Edward Lorenz, George David Birkhoff, Henri Jules, Marina Ratner, Princeton University Press, Proof Every, Proof Given, Steven Smale New!
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This chapter is a prelude to this book. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Intermediate-Value Theorem, Implicit-Function Theorem, Proof Let, Shadowing Theorem, Inverse-Function Theorem, New York, Anosov Closing Lemma, Cambridge University Press, Shadowing Lemma, American Mathematical Society, Hyperbolic Fixed-Point Theorem, Leonardo of Pisa, Annals of Mathematics, Mean-Value Theorem, Proof Suppose, Proof Take, Edward Lorenz, George David Birkhoff, Henri Jules, Marina Ratner, Princeton University Press, Proof Every, Proof Given, Steven Smale New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 27
books:
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1
book
cites this book:
- Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications) by Anatole Katok on 11 pages
- One-Dimensional Dynamics (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete 3 Folge) by Welington De Melo on page 306, page 314, and Back Matter
- Ordinary Differential Equations by V.I. Arnold in Back Matter (1), and Back Matter (2)
- Ordinary Differential Equations (Universitext) by Vladimir I. Arnold in Back Matter (1), and Back Matter (2)
- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen on page 237, and Back Matter
See all 27 books this book cites
- Elements of Applied Bifurcation Theory (Applied Mathematical Sciences) by Yuri Kuznetsov in Back Matter
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