动力系统复杂性与点串（英文）

Complexity of Dynamical System and Tuples

In this paper, we summarize our recent work on some complexity problems in dynamical systems related to chaos, entropy and recurrence properties under the ideas of localization (pairs or tuples). We solve a long open problem by proving that Devaney chaos implies Li-Yorke one. We show that there are ’many’ compacta admitting completely scrambled homeomorphisms, which include some countable compacta, the cantor set and continua of arbitrary dimension. Using the local notions of entropy: entropy tuples and sequence entropy pairs, we characterize the structures of a topological K- system and a topological null system. Finally, we give a ner classi cation of recurrence properties in terms of weak disjointness, complexity function of an open cover, and access time set.