Periodic shadowing and standard shadowing property

Darabi, Ali; Forouzanfar, Abdolmohammad

doi:10.1142/s1793557117500061

Cited by 7 publications

(5 citation statements)

References 10 publications

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“…In [6], Darabi and Fourouzanfar show that if f is an expansive map on a compact metric space and f has the shadowing property, then it has the periodic shadowing. We extend the result in uniform dynamical systems as follows:…”

Section: Resultsmentioning

confidence: 99%

“…It is shown in [6] that, if f is a chain transitive map on a compact metric space X and f has the periodic shadowing, then f has the shadowing property and so transitivity. We extend the result in uniform dynamical systems as follows:…”

Section: Resultsmentioning

confidence: 99%

“…In [6] it is shown that if f is chain mixing on a compact metric space, then f n is chain transitive for each n ≥ 1. The following theorem is the extension of the result in uniform dynamical systems.…”

Section: Resultsmentioning

confidence: 99%

“…In [6] Darabi and Fourounzanfer prove that, if f has periodic shadowing on compact metric space then so does f n for all n > 1. In the following, we extend the result in uniform dynamical systems.…”

Section: Resultsmentioning

confidence: 99%

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On periodic shadowing, transitivity, chain mixing and expansivity in uniform dynamical systems

Mangang

Akoijam

2020

GJOM

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In this paper we extend some results on the notions such as Expansive, Pseudo Orbit Tracing Property (P.O.T.P.), Chain Transitive, Periodic Shadowing, Chain Recurrent. We prove that if an expansive dynamical system (X,f) on compact uniform space has P.O.T.P., then it has periodic shadowing. If a continuous self map f on a compact uniform space has ﬁnite shadowing, then f has P.O.T.P. We ﬁnd that a dynamical system (X,f) on compact uniform space has shadowing property if (X,f) has periodic shadowing provided f is expansive. If f is chain mixing on a compact uniform space (X,U), then fn is chain transitive for each n ≥ 1. If f has the periodic shadowing then fn has periodic shadowing for all n > 1. The periodic shadowing is invariant of topological conjugacy provided that the conjugacy and its inverse are Lipschitz.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

On periodic shadowing, transitivity, chain mixing and expansivity in uniform dynamical systems

Mangang

Akoijam

2020

GJOM

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“…There is abundant research about shadowing property (See [13][14][15]). In addition, there are also other notions of shadowing that have been introduced, such as weak shadowing [16], orbital shadowing [17], eventually shadowing property [5,18], finite shadowing property [15], periodic shadowing [19,20], etc.…”

Section: Introductionmentioning

confidence: 99%

Measurable Version of Spectral Decomposition Theorem for a Z2-Action

Kamarudin

Dzul-Kifli

2023

Symmetry

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In this article, we present a measurable version of the spectral decomposition theorem for a Z2-action on a compact metric space. In the process, we obtain some relationships for a Z2-action with shadowing property and k-type weak extending property. Then, we introduce a definition of measure expanding for a Z2-action by using some properties of a Borel measure. We also prove one property that occurs whenever a Z2-action is invariantly measure expanding. All of the supporting results are necessary to prove the spectral decomposition theorem, which is the main result of this paper. More precisely, we prove that if a Z2-action is invariantly measure expanding, has shadowing property and has k-type weak extending property, then it has spectral decomposition.

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