Topological structure of G-non recurrent point and dynamical properties of G-average shadowing property(G-非回归点的拓扑结构和G-平均跟踪性的动力学性质)

Abstract

In this paper, we introduce the concepts of G-non recurrent point and G-average shadowing property. Then, we study the topological structure of G-non recurrent point in the inverse limit space under group action and the dynamical properties of G-average shadowing property in metric G-space. The results are as follows: (1) The self-map f has G-non recurrent point if and only if the shift map σ has G¯-non recurrent point; (2) If fk has G-average shadowing property, then f has G-average shadowing property. These results generalize the conclusions of non recurrent point set of shift mapping in the inverse limit space and average shadowing property of iterative mapping in metric space.(介绍了G-非回归点和G-平均跟踪性的概念，在群作用下的逆极限空间中研究了G-非回归点的拓扑结构，在度量G-空间中研究了G-平均跟踪性的动力学性质，得到：（1）自映射f有G-非回归点的充要条件是移位映射σ有G¯-非回归点；（2）如果fk具有G-平均跟踪性，则f具有G-平均跟踪性。这些结果推广了逆极限空间中移位映射非回归点集的结论以及度量空间中迭代映射平均跟踪性的结论。)

Keywords

• group action(群作用)
• inverse limit space(逆极限空间)
• g-non recurrent point(g-非回归点)
• g-average shadowing property(g-平均跟踪性)