Preface |
Introduction |
Carathéodory Dimension Characteristics / Part I: |
General Carathéodory Construction / Chapter 1: |
Carathéodory Dimension of Sets / 1: |
Carathéodory Capacity of Sets / 2: |
Carathéodory Dimension and Capacity of Measures / 3: |
Coincidence of Carathéodory Dimension and Carathéodory Capacity of Measures / 4: |
Lower and Upper Bounds for Carathéodory Dimension of Sets; Carathéodory Dimension Spectrum / 5: |
C-Structures Associated with Metrics: Hausdorff Dimension and Box Dimension / Chapter 2: |
Hausdorff Dimension and Box Dimension of Sets / 6: |
Hausdorff Dimension and Box Dimension of Measures; Pointwise Dimension; Mass Distribution Principle / 7: |
C-Structures Associated with Metrics and Measures: Dimension Spectra / Chapter 3: |
q-Dimension and q-Box Dimension of Sets / 8: |
q-Dimension and q-Box Dimension of Measures / 9: |
Hausdorff (Box) Dimension and Q-(Box) Dimension of Sets and Measures in General Metric Spaces / Appendix I: |
C-Structures Associated with Dynamical Systems: Thermodynamic Formalism / Chapter 4: |
A Modification of the General Carathéodory Construction / 10: |
Dimensional Definition of Topological Pressure; Topological and Measure-Theoretic Entropies / 11: |
Non-additive Thermodynamic Formalism / 12: |
Variational Principle for Topological Pressure; Symbolic Dynamical Systems; Bowen's Equation / Appendix II: |
An Example of Carathéodory Structure Generated by Dynamical Systems / Appendix III: |
Applications to Dimension Theory and Dynamical Systems / Part II: |
Dimension of Cantor-like Sets and Symbolic Dynamics / Chapter 5: |
Moran-like Geometric Constructions with Stationary (Constant) Ratio Coefficients / 13: |
Regular Geometric Constructions / 14: |
Moran-like Geometric Constructions with Non-stationary Ratio Coefficients / 15: |
Geometric Constructions with Rectangles; Non-coincidence of Box Dimension and Hausdorff Dimension of Sets / 16: |
Multifractal Formalism / Chapter 6: |
Correlation Dimension / 17: |
Dimension Spectra: Hentschel-Procaccia, Rényi, and f(alpha)-Spectra; Information Dimension / 18: |
Multifractal Analysis of Gibbs Measures on Limit Sets of Geometric Constructions / 19: |
Dimension of Sets and Measures Invariant under Hyperbolic Systems / Chapter 7: |
Hausdorff Dimension and Box Dimension of Conformal Repellers for Smooth Expanding Maps / 20: |
Multifractal Analysis of Gibbs Measures for Smooth Conformal Expanding Maps / 21: |
Hausdorff Dimension and Box Dimension of Basic Sets for Axiom A Diffeomrophisms / 22: |
Hausdorff Dimension of Horseshoes and Solenoids / 23: |
Multifractal Analysis of Equilibrium Measures on Basic Sets of Axiom A Diffeomorphisms / 24: |
A General Concept of Multifractal Spectra; Multifractal Rigidity / Appendix IV: |
Relations between Dimension, Entropy, and Lyapunov Exponents / Chapter 8: |
Existence and Non-existence of Pointwise Dimension for Invariant Measures / 25: |
Dimension of Measures with Non-zero Lyapunov Exponents; The Eckmann-Ruelle Conjecture / 26: |
Some Useful Facts / Appendix V: |
Bibliography |
Index |
Preface |
Introduction |
Carathéodory Dimension Characteristics / Part I: |