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Fractal Dimensions for Poincare Recurrences
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  • Fractal Dimensions for Poincare Recurrences
ID: 172404
Valentin Afraimovich, Edgardo Ugalde, Jesus Urias
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The system almost repeats its initial state. This book is devoted to an important branch of the dynamic system. 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 be used as a graduate text or a non-linear dynamics (in the natural sciences). Moreover, the book can be used by specialists in nonlinear dynamics. The authors of the problematic problems of chaotic systems.



* Portions of the book was published in the title of "Mathematics month in a field of Mathematics" in May 2004
* Rigorous mathematical theory is combined with important physical applications
* Presents rules for immediate action to mathematical models of real systems
* Contains standard theorems of dynamical systems theory

1. Introduction

Part 1: Fundamentals

2. Symbolic Systems
3. Geometric Constructions
4. Spectrum of Dimensions for Recurrences

Part II: Zero-Dimensional Invariant Sets

5. Uniformly Hyperbolic Repellers
6. Non-Uniformly Hyperbolic Repellers
7. The Spectrum for a Sticky Set
8. Rhythmical Dynamics

Part III: One-Dimensional Systems

9. Markov Maps of the Interval
10. Suspended Flows

Part IV: Measure Theoretical Results

11. Invariant Measures
12. Dimensional for Measures
13. The Variational Principle

Part V: Physical Interpretation and Applications

14. Intuitive Explanation
15. Hamiltonian Systems
16. Chaos Synchronization

Part VI: Appendices

17. Some Known Facts About Recurrences
18. Birkhoff's Individual Theorem
19. The SMB Theorem
20. Amalgamation and Fragmentation

index

172404

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