非自治动力系统中周期跟踪和极限跟踪的研究

The research of periodic shadowing and limit shadowing in nonautonomous dynamical systems

根据自治动力系统中周期跟踪性和极限跟踪性的定义,将其引入到非自治动力系统。研究了非自治动力系统中周期跟踪性和极限跟踪性的动力学性质,得到:(1)若F={f_i}_(i=0)~∞拓扑共轭于G={g_i}_(i=0)~∞,则F具有周期跟踪性当且仅当G具有周期跟踪性;(2)若F={f_i}_(i=0)~∞拓扑共轭于G={g_i}_(i=0)~∞,则F具有极限跟踪性当且仅当G具有极限跟踪性;(3)若乘积系统(X×Y,F×G)具有周期跟踪性,则(X,F)和(Y,G)具有周期跟踪性。以上结论对非自治动力系统中跟踪性的发展有一定的促进作用。

According to the definition of the periodic shadowing property and the limit shadowing property in autonomous dynamical systems,this paper introduces the concept of periodic shadowing property and limit shadowing property in nonautonomous dynamical systems,and studies the dynamical properties of both shadowing properties and limit shadowing property innonautonomous dynamical systems.The following results are obtained:(1)IfF={fi}∞/i=0 and G={gi}∞/i=0 are topologically conjugate,then F has periodic shadowing property if and only if G has periodic shadowing property;(2) If F={ fi}∞i=0 and G={gi}∞/i=0 are topologically conjugate,then F has limit shadowing property if and only if G has limit shadowing property;(3) If the product system (X × Y,F × G) has periodic shadowing property,then (X,F) and (Y,G) have periodic shadowing property.The above results have the positive effect on the development of the shadowing property in autonomous dynamical systems.