Shadowing and average shadowing properties for iterated function systems

Bahabadi, Alireza Zamani

doi:10.1515/gmj-2015-0008

Cited by 34 publications

(16 citation statements)

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“…Remark 1.1. If IF S(F ) has the strong shadowing property, then every generator has the shadowing property but its converse is not true (see Example 1.5 in [11]).…”

Section: Theorem 12 If a Homeomorphism Of A Compact Metric Space Hamentioning

confidence: 99%

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Two-Sided Limit Shadowing Property on Iterated Function Systems

Mohtashamipour¹,

Bahabadi²

2020

KgJMat

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In this article, we introduce the two-sided limit shadowing property on an iterated function system (IF S) and attain some results such as totally transitivity, and shadowing property. Also, by means of the strong shadowing property, we achieve topologically mixing for this IF S. Then, we study the strong two-sided limit shadowing property and obtain the topologically mixing property, immediately. Moreover, we find a criterion to obtain the two-sided limit shadowing property. The relationship between two-sided limit shadowing property and another kinds of shadowing was studied in [3] and [6]. Let us mention some notations and necessary definitions on ordinary dynamical systems and iterated function systems. One can see these definitions in [2], [5], [8], and [10] for dynamical systems with one generator. Let (X,d) be a compact metric space and f : X → X be a homeomorphism. Assume that ε and δ are positive integer numbers. A sequence {x i } i∈Z is said to be a

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“…Remark 1.1. If IF S(F ) has the strong shadowing property, then every generator has the shadowing property but its converse is not true (see Example 1.5 in [11]).…”

Section: Theorem 12 If a Homeomorphism Of A Compact Metric Space Hamentioning

confidence: 99%

“…This implies the inverse of Theorem C is not true. Moreover, IF S({f 0 , f 1 }) dose not have the strong shadowing property (see Example 1.3 in [11]). So, the inverse of Theorem B does not hold.…”

Section: Proposition 27 If If S(f ) Has the Strong Shadowing Propermentioning

confidence: 99%

Two-Sided Limit Shadowing Property on Iterated Function Systems

Mohtashamipour¹,

Bahabadi²

2020

KgJMat

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“…[3,4,8,9,11,15]. Over the last decade, shadowing and chaos for iterated function systems, have gained a lot of attention by many researchers and various interesting results have been obtained [1,2,7,13,19,20,22].…”

Section: Introductionmentioning

confidence: 99%

Hypercyclic operators for iterated function systems

Salman

Das

2021

Hacettepe Journal of Mathematics and Statistics

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“…Ahn et al [2] introduced the notion of persistent actions for finitely generated group action on compact metric spaces and studied its relation to the topological stability. Bahabadi [5] discussed the shadowing and average shadowing properties for iterated function systems. Wu et al [26] further studied some chain properties and average shadowing for iterated function systems and proved that an iterated function system with (asymptotic) average shadowing is chain mixing.…”

Section: Introductionmentioning

confidence: 99%

Recurrent sets and shadowing for finitely generated semigroup actions on metric spaces

Wu¹

2021

Hacettepe Journal of Mathematics and Statistics

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We introduce various new type of recurrent sets for finitely generated semigroups on noncompact metric spaces that are conjugacy invariant, and obtain some basic properties of chain recurrent sets for semigroups via these new definitions. Moreover, we define the notion of weak shadowing property for finitely generated group actions on compact metric spaces, which is weaker than that of shadowing property, and prove the equivalence of the shadowing and weak shadowing properties for the finitely generated group actions on a generalized homogeneous space without isolated points.

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Shadowing and average shadowing properties for iterated function systems

Cited by 34 publications

References 0 publications

Two-Sided Limit Shadowing Property on Iterated Function Systems

Two-Sided Limit Shadowing Property on Iterated Function Systems

Hypercyclic operators for iterated function systems

Recurrent sets and shadowing for finitely generated semigroup actions on metric spaces

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