非自治离散动力系统的强跟踪性

The Strongly Shadowing Property of the Nonautonomous Dynamical Systems

设(X,d)为度量空间,fk∶X→X,k=1,2…为一列连续映射,f0为单位映射,F={fk}∞k=0为X上的一个时变映射族,称(X,F)为非自治离散动力系统.因为非自治离散动力系统能够更能灵活地描述现实世界的一些动态,所以非自治离散动力系统的动力性态是人们最近所关注的重要问题.然而由于非自治离散动力系统要比自治离散动力系统更加复杂,因此,研究非自治离散动力系统的动力性态是比较困难的.通过在非自治离散动力系统中引进强跟踪性的概念,讨论了非自治离散动力系统强跟踪性的拓扑共轭不变性,并证明了有限个非自治离散动力系统的乘积系统具有强跟踪性的充分必要条件是每个非自治离散动力系统均具有强跟踪性.

Let （X,d）be compact metric space,fk： X→X,k = 1,2,., be a sequence of continuous map,f0 be identical map, and let F = {fk }km-0 be a time varying homeomorphisms on X, （ X, F） is called a nonautonomous dynamical systems. The study of dynamics of nonautonomous dynamical systems was widely concerned, because they are more flexible tools for the description of real world processes. While the study of dynamics of nonautonomous dynamical systems is ysyally more difficult than the same studies in the setting of autonomous dynamical systems. The strongly shadowing property for nonautonomous dynamical systems was studied. We proved that strongly shadowing property of nonautonomous dynamical system has topological conjugate invariance, by introducing the concept of the strongly shadowing property of nonautonomous dynamical system. And we also prove that the finite product of nonautonomous dynamical system has strongly shadowing property, if and only if each nonautonomous dynamical system has strongly shadowing property.