度量G-空间中G-强跟踪性和G-强链回归点的动力学性质

Dynamical properties of G-strong tracking property and G-strong chain recurrent point in metric G-spaces

首先,在度量G-空间中引入G-强跟踪性和G-强链回归点的概念;其次,分别在拓扑G-共轭条件下和提升空间中研究了它们的动力学性质和拓扑特征,得到如下结论:在拓扑G-共轭下,h(SCR_(G)(f_1))=SCR_(G)(f_2);在拓扑G-共轭下,f_(1)具有G-强跟踪性当且仅当f_(2)具有G-强跟踪性;在提升空间中,f具有G-强跟踪性当且仅当f具有G-强跟踪性.这些结果推广了强跟踪性和强链回归点集的结论.

Firstly,the concept of G-strong tracking property and G-strong chain recurrent point was introduced in metric G-spacej secondly,their dynamical properties and topological characteristics were studied under topological G-conjugate conditions and in the lift spaces respectively.The conclusions were as follows:under topological G-conjugate conditions,we had h(SCR_(G)(f_1))=SCR_(G)(f_2)under topological G-conjugate conditions,the map f_(1)had the G-strong tracking property if and only if the map f_(2)had the G-strong tracking property;in the lift spaces,the map/had the G-strong tracking property if and only if the map/had the G-strong tracking property.These results extended the conclusion of strong tracking property and strong chain recurrent point set.