Auslander-Yorke二分法、多灵敏度和李雅普诺夫数
Auslander-Yorke dichotomy theorem, multi-sensitivity and Lyapunov numbers
摘要：
本文研究了紧致度量空间上连续满射自映射的几种较强形式的灵敏性以及它们之间的关系。本文的主要结果表明，极小系统要么是其极大等度连续因子的多敏扩张，要么是其极大等度连续因子的几乎一对一扩张，这与Auslander-Yorke二分性定理类似.对于极小动力系统，我们还证明了厚灵敏度、多重灵敏度和厚综合灵敏度的概念是等价的，并且它们都比灵敏度强得多。
英文摘要：
In this paper we study several stronger forms of sensitivity for continuous surjective selfmaps on compact metric spaces and relations between them. The main result of the paper states that a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor, which is an analog of the Auslander-Yorke dichotomy theorem. For minimal dynamical systems, we also show that all notions of thick sensitivity, multi-sensitivity and thickly syndetical sensitivity are equivalent, and all of them are much stronger than sensitivity.
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