Dimension and Recurrence in Hyperbolic Dynamics

1. Introduction

2. Basic Notions

Part I. Dimension Theory

3. Dimension Theory and Thermodynamic Formalism

4. Repellers and Hyperbolic Sets

5. Measures of Maximal Dimension

Part II. Multifractal Analysis: Core Theory

6. Multifractal Analysis of Equilibrium Measures

7. General Concept of Multifractal Analysis

8. Dimension of Irregular Sets

9. Variational Principles in Multifractal Analysis

Part III. Multifractal Analysis: Further Developments

10. Multidimensional Spectra and Number Theory

11. Multifractal Rigidity

12. Hyperbolic Sets: Past and Future

Part IV. Hyperbolicity and Recurrence

13. Pointwise Dimension for Hyperbolic Dynamics

14. Product Structure of Hyperbolic Measures

15. Quantitative Recurrence and Dimension Theory

Keywords: MATHEMATICS / General MAT000000