关于半群作用是spatiotemporal混沌的几点注记

Some Remarks on the Spatiotemporal Chaos Behavior of Semigroup Actions

混沌理论是动力系统研究的重要课题之一,目前有关一个系统是混沌的定义已有多种,系统在何条件下出现何种混沌是混沌理论研究的一个重要方面。利用Li-Yorke点对,给出了半群作用的spatiotemporal混沌的定义,借助于族以及拓扑等相关知识,讨论混合性、2-刚性和spatio-temporal混沌之间的关系。证明了若(X,T)是拓扑弱混合的且T是交换半群,则系统(X,T)是ST混沌的。

Chaos is an important subject in dynamical system research,at present there are various criteria for whether a system is chaotic,and the relationship between chaos and topological properties is an important aspect of chaos theory.Based on Li-Yorke pairs,the definition of spatiotemporal chaos of semigroup actions was given.Using Furstenberg families,we studied the relations among the spatiotemporal chaos,mixing,and 2-rigidity,and we proved that topologically weakly mixing system implies ST chaos.