G-链连续点和G-极限跟踪性

G-chain Continuous Point and G-limit Shadowing Property

摘要

在度量G-空间中介绍了G-链连续点和G-极限跟踪性的概念，利用等价映射和交换群的性质，研究了G-链连续点和G-极限跟踪性的动力学性质，得到如下结果：（1）在度量G-空间中给出X中每个点是G-链连续点等价条件：映射f是G-等度连续的并且f具有G-跟踪性；（2）G-扩张性和G-跟踪性蕴涵G-极限跟踪性。这些结果丰富了度量G-空间中G-链连续点和G-极限跟踪性的理论。

Abstract

We introduced the concepts of G-chain continuous poin and G-limit shadowing property in metric G-space. By using the properties of equivariant map and commutative group, we studied the dynamical properties of G-chain continuous poin and G-limit shadowing property, and obtained the following results. (1)The equivalent condition is given for every point to be G-chain continuous. That is, the map f is G-equicontinuous and has G-shadowing property in metric G-space; (2) G-expansivity and G-shadowing property imply G-limit shadowing property. These results enrich the theory of G-chain continuous point and G-limit shadowing property in metric G-space.

关键词

G-等度连续 / G-链连续点 / G-扩张性 / G-极限跟踪性 / G-跟踪性

Key words

G-equicontinuity / G-chain continuous point / G-expansivity / G-limit shadowing property / G-shadowing property

基金资助

国家自然科学基金(12126415)

广西自然科学基金(2020JJA110021)

梧州市科技计划项目(2024C03015)