Dimension theory in dynamical systems : contemporary views and applications /
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| Author / Creator: | Pesin, Ya. B. |
|---|---|
| Imprint: | Chicago : University of Chicago Press, 1997. |
| Description: | xi, 304 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | Chicago lectures in mathematics series Chicago lectures in mathematics. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/2919057 |
Table of Contents:
- Preface
- Introduction
- Part I. Carathéodory Dimension Characteristics
- Chapter 1. General Carathéodory Construction
- 1. Carathéodory Dimension of Sets
- 2. Carathéodory Capacity of Sets
- 3. Carathéodory Dimension and Capacity of Measures
- 4. Coincidence of Carathéodory Dimension and Carathéodory Capacity of Measures
- 5. Lower and Upper Bounds for Carathéodory Dimension of Sets; Carathéodory Dimension Spectrum
- Chapter 2. C-Structures Associated with Metrics: Hausdorff Dimension and Box Dimension
- 6. Hausdorff Dimension and Box Dimension of Sets
- 7. Hausdorff Dimension and Box Dimension of Measures; Pointwise Dimension; Mass Distribution Principle
- Chapter 3. C-Structures Associated with Metrics and Measures: Dimension Spectra
- 8. q-Dimension and q-Box Dimension of Sets
- 9. q-Dimension and q-Box Dimension of Measures
- Appendix I. Hausdorff (Box) Dimension and Q-(Box) Dimension of Sets and Measures in General Metric Spaces
- Chapter 4. C-Structures Associated with Dynamical Systems: Thermodynamic Formalism
- 10. A Modification of the General Carathéodory Construction
- 11. Dimensional Definition of Topological Pressure; Topological and Measure-Theoretic Entropies
- 12. Non-additive Thermodynamic Formalism
- Appendix II. Variational Principle for Topological Pressure; Symbolic Dynamical Systems; Bowen's Equation
- Appendix III. An Example of Carathéodory Structure Generated by Dynamical Systems
- Part II. Applications to Dimension Theory and Dynamical Systems
- Chapter 5. Dimension of Cantor-like Sets and Symbolic Dynamics
- 13. Moran-like Geometric Constructions with Stationary (Constant) Ratio Coefficients
- 14. Regular Geometric Constructions
- 15. Moran-like Geometric Constructions with Non-stationary Ratio Coefficients
- 16. Geometric Constructions with Rectangles; Non-coincidence of Box Dimension and Hausdorff Dimension of Sets
- Chapter 6. Multifractal Formalism
- 17. Correlation Dimension
- 18. Dimension Spectra: Hentschel-Procaccia, Rényi, and f(alpha)-Spectra; Information Dimension
- 19. Multifractal Analysis of Gibbs Measures on Limit Sets of Geometric Constructions
- Chapter 7. Dimension of Sets and Measures Invariant under Hyperbolic Systems
- 20. Hausdorff Dimension and Box Dimension of Conformal Repellers for Smooth Expanding Maps
- 21. Multifractal Analysis of Gibbs Measures for Smooth Conformal Expanding Maps
- 22. Hausdorff Dimension and Box Dimension of Basic Sets for Axiom A Diffeomrophisms
- 23. Hausdorff Dimension of Horseshoes and Solenoids
- 24. Multifractal Analysis of Equilibrium Measures on Basic Sets of Axiom A Diffeomorphisms
- Appendix IV. A General Concept of Multifractal Spectra; Multifractal Rigidity
- Chapter 8. Relations between Dimension, Entropy, and Lyapunov Exponents
- 25. Existence and Non-existence of Pointwise Dimension for Invariant Measures
- 26. Dimension of Measures with Non-zero Lyapunov Exponents; The Eckmann-Ruelle Conjecture
- Appendix V. Some Useful Facts
- Bibliography
- Index
