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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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Hindawi Limited
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/8140eeefce26400492a1abd74028d635 |
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| Sumario: | 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. |
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