Dynamical Property of the Shift Map under Group Action

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 t...

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Main Author: Zhanjinag Ji
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2022/5969042
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author Zhanjinag Ji
author_facet Zhanjinag Ji
author_sort Zhanjinag Ji
collection DOAJ
description 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.
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spelling doaj-art-d050498f8c3d4fabae2c8172bc7e0d862025-08-20T02:20:05ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/5969042Dynamical Property of the Shift Map under Group ActionZhanjinag Ji0School of Data Science and Software EngineeringFirstly, 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.http://dx.doi.org/10.1155/2022/5969042
spellingShingle Zhanjinag Ji
Dynamical Property of the Shift Map under Group Action
Advances in Mathematical Physics
title Dynamical Property of the Shift Map under Group Action
title_full Dynamical Property of the Shift Map under Group Action
title_fullStr Dynamical Property of the Shift Map under Group Action
title_full_unstemmed Dynamical Property of the Shift Map under Group Action
title_short Dynamical Property of the Shift Map under Group Action
title_sort dynamical property of the shift map under group action
url http://dx.doi.org/10.1155/2022/5969042
work_keys_str_mv AT zhanjinagji dynamicalpropertyoftheshiftmapundergroupaction