Fractal Dimensions for Poincare Recurrences - 1st Edition - ISBN: 9780444521897, 9780080462394

Fractal Dimensions for Poincare Recurrences, Volume 2

1st Edition

Authors: Valentin Afraimovich Edgardo Ugalde Jesus Urias
eBook ISBN: 9780080462394
Hardcover ISBN: 9780444521897
Imprint: Elsevier Science
Published Date: 21st June 2006
Page Count: 258
Tax/VAT will be calculated at check-out
15% off
15% off
15% off
15% off
149.00
126.65
200.00
170.00
120.00
102.00
185.00
157.25
Unavailable
File Compatibility per Device

PDF, EPUB, VSB (Vital Source):
PC, Apple Mac, iPhone, iPad, Android mobile devices.

Mobi:
Amazon Kindle eReader.

Institutional Access


Table of 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
    Index

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.

Key Features

  • 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

Readership

Researchers, lecturers and students in Nonlinear, Statistical and Mathematical Physics


Details

No. of pages:
258
Language:
English
Copyright:
© Elsevier Science 2006
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080462394
Hardcover ISBN:
9780444521897

About the Authors

Valentin Afraimovich Author

The authors started to work on the subject in 1997 because of requirements in nonlinear dynamics to find out quantities that could measure different behavior in time in dynamical systems. They introduced and studied fractal dimensions for Poincare recurrences that appeared to be new, useful characteristics of complexity of dynamics.

Affiliations and Expertise

Universidad Autonoma de San Luis Potosi, Mexico.

Edgardo Ugalde Author

The authors started to work on the subject in 1997 because of requirements in nonlinear dynamics to find out quantities that could measure different behavior in time in dynamical systems. They introduced and studied fractal dimensions for Poincare recurrences that appeared to be new, useful characteristics of complexity of dynamics.

Affiliations and Expertise

Universidad Autonoma de San Luis Potosi, Mexico.

Jesus Urias Author

The authors started to work on the subject in 1997 because of requirements in nonlinear dynamics to find out quantities that could measure different behavior in time in dynamical systems. They introduced and studied fractal dimensions for Poincare recurrences that appeared to be new, useful characteristics of complexity of dynamics.

Affiliations and Expertise

Universidad Autonoma de San Luis Potosi, Mexico.