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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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| 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. |
| format | Article |
| id | doaj-art-d050498f8c3d4fabae2c8172bc7e0d86 |
| institution | OA Journals |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| 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 |