| Description |
1 online resource (xi, 245 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Monograph series on nonlinear science and complexity, 1574-6917 ; v. 2 |
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Monograph series on nonlinear science and complexity ; v. 2. 1574-6917
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| Summary |
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 |
| 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. |
| Bibliography |
Includes bibliographical references and index. |
| Note |
Print version record. |
| Language |
English. |
| Subject |
Fractals.
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Poincaré series.
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Fractales.
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Séries de Poincaré.
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fractals.
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MATHEMATICS -- Topology.
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Fractals
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Poincaré series
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| Added Author |
Ugalde, E. (Edgardo)
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Urías, J. (Jesús)
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| Other Form: |
Print version: Aframovich, V.S. (Valentin Senderovich). Fractal dimensions for Poincaré recurrences. Amsterdam ; London : Elsevier, 2006 0444521895 9780444521897 (OCoLC)64959093 |
| ISBN |
9780444521897 |
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0444521895 |
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0080462391 (electronic bk.) |
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9780080462394 (electronic bk.) |
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1280641851 |
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9781280641855 |
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9786610641857 |
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6610641854 |
| Standard No. |
AU@ 000048129539 |
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DEBBG BV042311050 |
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DEBSZ 27748801X |
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DEBSZ 430357281 |
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DEBSZ 482353945 |
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NZ1 12434652 |
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YDXCP 2501690 |
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AU@ 000072990080 |
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