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