On partial shadowing of complete pseudo-orbits

Oprocha, Piotr; Dastjerdi, Dawoud Ahmadi; Hosseini, Maryam

doi:10.1016/j.jmaa.2013.08.062

Cited by 14 publications

(18 citation statements)

References 15 publications

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“…In addition, it is known that shadowing property and regularly recurrent point have always been the focus of topological dynamical systems. At present, many scholars have studied them in the inverse limit space and obtained valuable research results (see [9][10][11][12][13][14][15]). But there are few research results about them in the double inverse limit space.…”

Section: Introductionmentioning

confidence: 99%

The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space

2022

Journal of Function Spaces

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According to the definition of sequence shadowing property and regularly recurrent point in the inverse limit space, we introduce the concept of sequence shadowing property and regularly recurrent point in the double inverse limit space and study their dynamical properties. The following results are obtained: (1) Regularly recurrent point sets of the double shift map σ f ∘ σ g are equal to the double inverse limit space of the double self-map f ∘ g in the regularly recurrent point sets. (2) The double self-map f ∘ g has sequence shadowing property if and only if the double shift map σ f ∘ σ g has sequence shadowing property. Thus, the conclusions of sequence shadowing property and regularly recurrent point are generalized to the double inverse limit space.

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Section: Introductionmentioning

confidence: 99%

The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space

2022

Journal of Function Spaces

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“…Expansibility and shadowing property have attracted the attention of many scholars. e relevant results are seen in [11][12][13][14][15][16][17]. Das and Das [11] pointed out that the map f is G−expansive if and only if the map g is G−expansive in locally equidistant covered space.…”

Section: Introductionmentioning

confidence: 99%

“…Wu [16] proved that the system with d−tracking property is chain mixed. Oprocha et al [17] analyzed necessary and sufficient conditions for shadowing property over a set with positive density. In this paper, we gave the concepts of G−expansive map and G−limit shadowing property according to the concepts of expansive map and limit shadowing property.…”

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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“…They also mentioned that in chain-transitive systems, the thick shadowing property implies the shadowing property (see [6, p. 3764]). Later, an example was provided in [12] whereby the thick shadowing property can exist in a non-mixing dynamical system. Finally, [4] proved that in (chain-)transitive dynamical systems shadowing and thick shadowing are equivalent notions.…”

Section: Introductionmentioning

confidence: 99%

Shadowing, thick sets and the Ramsey property

Oprocha¹

2015

Ergod. Th. Dynam. Sys.

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We provide a full characterization of relations between the shadowing property and the thick shadowing property. We prove that they are equivalent properties for non-wandering systems, the thick shadowing property is always a consequence of the shadowing property, and the thick shadowing property on the chain-recurrent set and the thick shadowing property are the same properties. We also provide a full characterization of the cases when for any family ${\mathcal{F}}$ with the Ramsey property an arbitrary sequence of points can be ${\it\varepsilon}$-traced over a set from ${\mathcal{F}}$.

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On partial shadowing of complete pseudo-orbits

Cited by 14 publications

References 15 publications

The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space

The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space

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

Shadowing, thick sets and the Ramsey property

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