Complexity and proper quasi-weakly almost periodic points

Wang, Lidong; Li, Nan; Wang, Hui; Liang, Jianhua

doi:10.1016/j.chaos.2020.109884

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“…A point x is called to be an almost periodic point if for each open set U containing x there exists a positive integer m > 0 such that for every positive integer k > 0 there exists r ∈ (k, k + m] satisfying f r (x) ∈ U(see [1]). In recent years, there are many achievements about almost periodic points set (see [1][2][3][4][5][6][7][8]). Qiu and Zhao [2] proved that if the map f has shadowing property in X, then the map f has shadowing property in AP(f).…”

Section: Introductionmentioning

confidence: 99%

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

2021

Mathematical Problems in Engineering

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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 X f , 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 A P G ¯ σ = Lim ← A p G f , 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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Section: Introductionmentioning

confidence: 99%

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

2021

Mathematical Problems in Engineering

View full text Add to dashboard Cite

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Complexity and proper quasi-weakly almost periodic points

Cited by 1 publication

References 14 publications

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

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

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