摘要
设(X,f)是一个拓扑动力系统,X/R是X的一个商空间,那么由f可诱导出一个连续映射F:X/R→X/R,从而得到一个动力系统(X/R,F),本文称这样的系统为商系统。文中讨论了一个动力系统与它的商系统的周期稠密性、混沌性以及拓扑混合性之间的相互关系,得到了这些性质分别是相互等价的等结论,从而得到了研究动力系统混沌性的一个重方法。
Let （X, f） be a dynamic system, X/R a quotient space of X, then there is a continuous map F： X/R→X/R reduced by f, so another dynamic system （X/R, F） called quotient system in this paper is gained. In this paper, the relationship of the properties of periodic density, chaos and topological mixing between a dynamic system and its quotient system is discussed, and we get the conclusion that those properties are equivalent respectively, so an important method to study the chaos of a dynamic system is gained.
出处
《衡阳师范学院学报》
2006年第6期11-13,共3页
Journal of Hengyang Normal University
基金
湖南省教育厅资助项目(2006)
衡阳师范学院教改课题
关键词
混沌
周期点
商系统
拓扑混合
chaos, periodic point, quotient system topological mixing
