Dimension theory in dynamical systems: contemporary views and applications

Contents......Page 0
Preface......Page 10
Introduction......Page 14
Part I Caratheodory Dimension Characteristics......Page 22
1 General Caratheodory Construction......Page 24
2 C-Structures Associated with Metrics: Hausdorff Dimension and Box Dimension......Page 47
3 C-Structures Associated with Metrics and Measures: Dimension Spectra......Page 61
A-I Hausdorff (Box) Dimension and q-(Box) Dimension of Sets and Measures in General Metric Spaces......Page 74
4 C-Structures Associated with Dynamical Systems: Thermodynamic Formalism......Page 77
A-II Variational Principle for Topological Pressure; Symbolic Dynamical Systems; Bowen\'s Equation......Page 100
A-III An Example of Caratheodory Structure Generated by Dynamical Systems......Page 123
Part II Applications to Dimension Theory and Dynamical Systems......Page 128
5 Dimension of Cantor-like Sets and Symbolic Dynamics......Page 130
6 Multifractal Formalism......Page 183
7 Dimension of Sets and Measures Invariant under Hyperbolic Systems......Page 209
A-IV A General Concept of M ultifractal Spectra; M ultifractal Rigidity......Page 272
8 Relations between Dimension, Entropy, and Lyapunov Exponents......Page 283
A-V Some Useful Information......Page 306
Bibliography......Page 308
Index......Page 314