非自治动力系统中逐点跟踪性和极限跟踪的研究

The Research of Pointwise Shadowing Property and Limit Shadowing Property in Nonautonomous Dynamical Systems

根据离散动力系统中逐点跟踪性和极限跟踪性的定义,引入非自治动力系统中逐点跟踪性和极限跟踪性的概念,研究了非自治动力系统中逐点跟踪性和极限跟踪性的动力学性质,得到如下结果:1)若F={fi}i=0^∞拓扑共轭于G={gi}i=0^∞,则F具有逐点跟踪性当且仅当G具有逐点跟踪性;2)乘积系统(X×Y,F×G)具有逐点跟踪性当且仅当(X,F)和(Y,G)具有逐点跟踪性;3)乘积系统(X×Y,F×G)具有极限跟踪性当且仅当(X,F)和(Y,G)具有极限跟踪性.这些结果丰富了非自治动力系统中逐点跟踪性和极限跟踪性的理论.

According to the definition of pointwise shadowing property and limit shadowing property in autonomous dynamical systems,it is introduced that the concept of pointwise shadowing property and limit shadowing property in nonautonomous dynamical systems.We study the dynamic properties of pointwise shadowing property and limit shadowing property in nonautonomous dynamical systems.The following results are obtained:(1) If F={fi}i=0∞and G={gi}i=0∞are to be topologically conjugate,then F has pointwise shadowing property if and only if G has pointwise shadowing property;(2) The product system(X x Y,F x G)has pointwise shadowing property if and only if(X,F) and(Y,G) have pointwise shadowing property;(3) The product system(X x Y,F x G) has limit shadowing property if and only if(X,F) and(Y,G) have limit shadowing property.These results enrich the theory of pointwise shadowing property and limit shadowing property in nonautonomous dynamical systems.