Fractal Dimensions for Poincare Recurrences

Informationen zum Autor 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. 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. 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. Zusammenfassung Deals with 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. This book presents rules for action to study mathematical models of real systems. It contains standard theorems of dynamical systems theory.

List of contents

1. IntroductionPart 1: Fundamentals2. Symbolic Systems3. Geometric Constructions4. Spectrum of Dimensions for RecurrencesPart II: Zero-Dimensional Invariant Sets5. Uniformly Hyperbolic Repellers6. Non-Uniformly Hyperbolic Repellers7. The Spectrum for a Sticky Set8. Rhythmical DynamicsPart III: One-Dimensional Systems9. Markov Maps of the Interval10. Suspended FlowsPart IV: Measure Theoretical Results11. Invariant Measures12. Dimensional for Measures13. The Variational PrinciplePart V: Physical Interpretation and Applications14. Intuitive Explanation15. Hamiltonian Systems16. Chaos SynchronizationPart VI: Appendices17. Some Known Facts About Recurrences18. Birkhoff's Individual Theorem19. The SMB Theorem20. Amalgamation and FragmentationIndex

Product details

• Authors: Valentin Afraimovich, Valentin (San Luis Potosi State Unive Afraimovich, Valentin (Universidad Autonoma De San Afraimovich, Valentin (Universidad Autonoma de San Luis Potosi Afraimovich, Afraimovich Valentin, E. Ugalde, Edgardo Ugalde, Edgardo (Universidad Autonoma de San Luis Potosi Ugalde, Ugalde Edgardo, J. Urias, Jesus Urias, Jesus (Universidad Autonoma de San Luis Potosi Urias, Urias Jesus
• Publisher: ELSEVIER SCIENCE BV
• Languages: English
• Product format: Hardback
• Released: 21.06.2006
• EAN: 9780444521897
• ISBN: 978-0-444-52189-7
• No. of pages: 258
• Series: Monograph Series on Nonlinear; Monograph Series on Nonlinear Science and Complexity; Monograph Series on Nonlinear
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; SCIENCE / Physics / General, MATHEMATICS / Applied, MATHEMATICS / Mathematical Analysis, Physics, Calculus & mathematical analysis, Applied mathematics, Calculus and mathematical analysis