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Pincaré Recurrence and Measure-theoretic Entropy in Dynamical Systems

摘要第4-5页
Abstract第5页
Chapter 1 Introduction第6-10页
    §1.1 Introduction of Poincaré recurrence and Multifractal analysis第6-9页
    §1.2 Main results第9-10页
Chapter 2 Multifractal analysis of local entropies for a-weighted entropy第10-22页
    §2.1 The definitions of a-weighted entropy第10-13页
    §2.2 (a,q,μ)-entropy of non-compact or non-invariant sets,weighted en-tropy doubling condition第13-17页
    §2.3 Proof of the main result第17-22页
Chapter 3 Ornstein-Weiss theorem for r-ball第22-30页
    §3.1 Preliminaries第22-24页
    §3.2 Ornstein-Weiss theorem for r-ball第24-30页
Chapter 4 Poincaré recurrence and a-weighted entropy第30-42页
    §4.1 Return times to a-weighted partition and a-weighted entropy第30-36页
    §4.2 Return times to a-weighted Bowen ball and a-weighted entropy第36-42页
Bibliography第42-45页
致谢第45页

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