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By Valentin Afraimovich, Universidad Autonoma de San Luis Potosi, Mexico. Edgardo Ugalde, Universidad Autonoma de San Luis Potosi, Mexico. Jesus Urias, Universidad Autonoma de San Luis Potosi, Mexico.
Description 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.
Audience
Researchers, lecturers and students in Nonlinear, Statistical and Mathematical Physics
Contents 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
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