G-Expansibility and G-Almost Periodic Point under Topological Group Action

Firstly, the new concepts of G−expansibility, G−almost periodic point, and G−limit shadowing property were introduced according to the concepts of expansibility, almost periodic point, and limit shadowing property in this paper. Secondly, we studied their dynamical relationship between the self-map...

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Autor principal:	Zhanjiang Ji
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8140eeefce26400492a1abd74028d635
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spelling	oai:doaj.org-article:8140eeefce26400492a1abd74028d6352021-11-22T01:09:29ZG-Expansibility and G-Almost Periodic Point under Topological Group Action1563-514710.1155/2021/7326623https://doaj.org/article/8140eeefce26400492a1abd74028d6352021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/7326623https://doaj.org/toc/1563-5147Firstly, the new concepts of G−expansibility, G−almost periodic point, and G−limit shadowing property were introduced according to the concepts of expansibility, almost periodic point, and limit shadowing property in this paper. Secondly, we studied their dynamical relationship between the self-map f and the shift map σ in the inverse limit space under topological group action. The following new results are obtained. Let X,d be a metric G−space and Xf,G¯, d¯,σ be the inverse limit space of X,G,d,f. (1) If the map f:X⟶X is an equivalent map, then we have APG¯σ=Lim←ApGf,f. (2) If the map f:X⟶X is an equivalent surjection, then the self-map f is G−expansive if and only if the shift map σ is G¯−expansive. (3) If the map f:X⟶X is an equivalent surjection, then the self-map f has G− limit shadowing property if and only if the shift map σ has G¯− limit shadowing property. The conclusions of this paper generalize the corresponding results given in the study by Li, Niu, and Liang and Li . Most importantly, it provided the theoretical basis and scientific foundation for the application of tracking property in computational mathematics and biological mathematics.Zhanjiang JiHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Zhanjiang Ji G-Expansibility and G-Almost Periodic Point under Topological Group Action
description	Firstly, the new concepts of G−expansibility, G−almost periodic point, and G−limit shadowing property were introduced according to the concepts of expansibility, almost periodic point, and limit shadowing property in this paper. Secondly, we studied their dynamical relationship between the self-map f and the shift map σ in the inverse limit space under topological group action. The following new results are obtained. Let X,d be a metric G−space and Xf,G¯, d¯,σ be the inverse limit space of X,G,d,f. (1) If the map f:X⟶X is an equivalent map, then we have APG¯σ=Lim←ApGf,f. (2) If the map f:X⟶X is an equivalent surjection, then the self-map f is G−expansive if and only if the shift map σ is G¯−expansive. (3) If the map f:X⟶X is an equivalent surjection, then the self-map f has G− limit shadowing property if and only if the shift map σ has G¯− limit shadowing property. The conclusions of this paper generalize the corresponding results given in the study by Li, Niu, and Liang and Li . Most importantly, it provided the theoretical basis and scientific foundation for the application of tracking property in computational mathematics and biological mathematics.
format	article
author	Zhanjiang Ji
author_facet	Zhanjiang Ji
author_sort	Zhanjiang Ji
title	G-Expansibility and G-Almost Periodic Point under Topological Group Action
title_short	G-Expansibility and G-Almost Periodic Point under Topological Group Action
title_full	G-Expansibility and G-Almost Periodic Point under Topological Group Action
title_fullStr	G-Expansibility and G-Almost Periodic Point under Topological Group Action
title_full_unstemmed	G-Expansibility and G-Almost Periodic Point under Topological Group Action
title_sort	g-expansibility and g-almost periodic point under topological group action
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/8140eeefce26400492a1abd74028d635
work_keys_str_mv	AT zhanjiangji gexpansibilityandgalmostperiodicpointundertopologicalgroupaction
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G-Expansibility and G-Almost Periodic Point under Topological Group Action

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