Dynamical Property of the Shift Map under Group Action

Author:

Ji Zhanjinag123ORCID

Affiliation:

1. School of Data Science and Software Engineering, Wuzhou University, Wuzhou, Guangxi 543002, China

2. Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou University, Wuzhou, Guangxi 543002, China

3. Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Wuzhou, Guangxi 543002, China

Abstract

Firstly, we introduced the concept of G Lipschitz tracking property, G asymptotic average tracking property, and G periodic tracking property. Secondly, we studied their dynamical properties and topological structure and obtained the following conclusions: (1) let X , d be compact metric G space and the metric d be invariant to G . Then, σ has G ¯ asymptotic average tracking property; (2) let X , d be compact metric G space and the metric d be invariant to G . Then, σ has G ¯ Lipschitz tracking property; (3) let X , d be compact metric G space and the metric d be invariant to G . Then, σ has G ¯ periodic tracking property. The above results make up for the lack of theory of G Lipschitz tracking property, G asymptotic average tracking property, and G periodic tracking property in infinite product space under group action.

Funder

Wuzhou University

Publisher

Hindawi Limited

Subject

Applied Mathematics,General Physics and Astronomy

Reference20 articles.

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4. Sub-shadowings

5. On shadowing: Ordinary and ergodic

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