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Fractal Dimensions for Poincare Recurrences
Fractal Dimensions for Poincare Recurrences
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Fractal Dimensions for Poincare Recurrences

Valentin Afraimovich, Edgardo Ugalde, Jesus Urias
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258 pages
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English
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Fractal Dimensions for Poincare Recurrences

Valentin Afraimovich, Edgardo Ugalde, Jesus Urias
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About This Book

This book is devoted to an important branch of the dynamical systems theory: the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the book can be used by specialists in applied nonlinear dynamics following the way in the book. The authors applied the mathematical theory developed in the book to two important problems: distribution of Poincare recurrences for nonpurely chaotic Hamiltonian systems and indication of synchronization regimes in coupled chaotic individual systems.

* Portions of the book were published in an article that won the title "month's new hot paper in the field of Mathematics" in May 2004
* Rigorous mathematical theory is combined with important physical applications
* Presents rules for immediate action to study mathematical models of real systems
* Contains standard theorems of dynamical systems theory

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Information

Publisher
Elsevier Science
Year
2006
ISBN
9780080462394
Topic
Physical Sciences
Subtopic
Mathematical & Computational Physics

Table of contents