Invariants of topological G-conjugacy on G-spaces

Ahmadi, Seyyed Alireza

doi:10.5937/matmor1401067a

Cited by 17 publications

(5 citation statements)

References 4 publications

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“…The data used to support the findings of this study are included within references [1][2][3][4][5][6][7][8][9][10][11][12][13][14] in the article.…”

Section: Discussionmentioning

confidence: 99%

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$G$ -Chain Mixing and $G$ -Chain Transitivity in Metric G-Space

2022

Advances in Mathematical Physics

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Firstly, we introduce the concept of G -chain mixing, G -mixing, and G -chain transitivity in metric G -space. Secondly, we study their dynamical properties and obtain the following results. (1) If the map f has the G -shadowing property, then the map f is G -chain mixed if and only if the map f is G -mixed. (2) The map f is G -chain transitive if and only if for any positive integer k ≥ 2 , the map f k is G -chain transitive. (3) If the map f is G -pointwise chain recurrent, then the map f is G -chain transitive. (4) If there exists a nonempty open set U satisfying G U = U , U ¯ ≠ X , and f U ¯ ⊂ U , then we have that the map f is not G -chain transitive. These conclusions enrich the theory of G -chain mixing, G -mixing, and G -chain transitivity in metric G -space.

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“…The data used to support the findings of this study are included within references [1][2][3][4][5][6][7][8][9][10][11][12][13][14] in the article.…”

Section: Discussionmentioning

confidence: 99%

“…G-Space Definition 5 (see [10]). Let ðX, dÞ be a metric G-space, G be a topological group, and φ : G × X ⟶ X be a continuous map.…”

Section: G-chain Mixing and G-mixing In Metricmentioning

confidence: 99%

$G$ -Chain Mixing and $G$ -Chain Transitivity in Metric G-Space

2022

Advances in Mathematical Physics

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“…The concept of G Strongly uniform converge is seen in [15]. The concept of metric G space can be found in [16].…”

Section: G-almost Periodic Point Setmentioning

confidence: 99%

The Research of G-Almost Periodic Point

Bei

2022

Advances in Transdisciplinary Engineering

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Firstly, it is introduced that the concepts of G-almost periodic point and G-sequence shadowing property. Then, we discuss the dynamical relationship between sequence map {gk}∞k=1 and limit map g under G-strongly uniform convergence of topological group action. We can get that (1) Let sequence map {gk}∞k=1 be G-strongly uniform converge to the map g where g is equicontinuous and the point sequence {yk}∞k=1 be the G-almost periodic point of sequence map {gk}∞k=1. If limk → ∞ yk = y, then the point y is an G-almost periodic point of the map g; (2) If sequence map {gk}∞k=1 are G-strongly uniform converge to the map g where g is equicontinuous, then limsup APG(gk) ⊂ APG(g); (3) Let sequence map {gk}∞k=1 be G-strongly uniform converge to the map g. If every map gk has G-fine sequence shadowing property, the map g has G-sequence shadowing property. These results generalize the corresponding results given in Ji and Zhang [1] and make up for the lack of theory under G-strongly uniform convergence of group action.

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“…The concept of metric G-space is shown in [12]. We can find the concept that d is invariant to G in [13].…”

Section: G-asymptotic Average Shadowing Property Of σmentioning

confidence: 99%

“…The data used to support the findings of this study are included within references [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] in the article.…”

mentioning

confidence: 99%

Dynamical Property of the Shift Map under Group Action

2022

Advances in Mathematical Physics

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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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Invariants of topological G-conjugacy on G-spaces

Abstract: Abstract. In this paper we present invariant dynamical properties under G-conjugacy. Moreover we introduce the notions of G-minimal systems, strong G-shadowing property and limit G-shadowing property and we show that these properties are invariant under topological Gconjugacy.

Cited by 17 publications

References 4 publications

$G$ -Chain Mixing and $G$ -Chain Transitivity in Metric G-Space

$G$ -Chain Mixing and $G$ -Chain Transitivity in Metric G-Space

The Research of G-Almost Periodic Point

Dynamical Property of the Shift Map under Group Action

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Invariants of topological G-conjugacy on G-spaces

Abstract: Abstract. In this paper we present invariant dynamical properties under G-conjugacy. Moreover we introduce the notions of G-minimal systems, strong G-shadowing property and limit G-shadowing property and we show that these properties are invariant under topological Gconjugacy.

Cited by 17 publications

References 4 publications

G -Chain Mixing and G -Chain Transitivity in Metric G-Space

G -Chain Mixing and G -Chain Transitivity in Metric G-Space

The Research of G-Almost Periodic Point

Dynamical Property of the Shift Map under Group Action

Contact Info

Product

Resources

About

$G$ -Chain Mixing and $G$ -Chain Transitivity in Metric G-Space

$G$ -Chain Mixing and $G$ -Chain Transitivity in Metric G-Space