Chain Mixing and Chain Transitive Iterated Function Systems

Nia, Mehdi Fatehi

doi:10.1080/1726037x.2020.1856338

Cited by 2 publications

(4 citation statements)

References 10 publications

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“…Fatehi Nia [15] confirmed that shadowing is invariant under a topological conjugacy and that T n have shadowing property if T have shadowing property. He provides sufficient conditions for an IFS to have shadowing property.…”

Section: Topological Shadowing Property Of Iterated Function Systemsmentioning

confidence: 90%

“…In [16], Richeson and Wiseman proved that the chain mixing, totally chain transitive, chain transitive, and chain recurrent properties of a dynamical system (T, g) are equivalent over a connected metric space T . Mehdi [15] extended this equivalence on iterated function systems. Recently, Ahmadi et al [2] proved that the TCM, TTCT, TCT, and TCR properties of a dynamical system over a connected compact uniform space are equivalent.…”

Section: Theorem 44 Let T Be An Ifs On a Compact Uniform Space (T U) ...mentioning

confidence: 92%

“…Fatehi Nia [15] introduced the following definitions of topological transitive, topological mixing, and totally topological transitive iterated function systems. He also introduced the notion of topological conjugacy of iterated function systems.…”

Section: Preliminariesmentioning

confidence: 99%

“…The following theorem is an extension of [14], [Proposition 2.15] in IFS on a compact uniform space. Fatehi Nia [15] proved the following theorem as a lemma in iterated function systems. Here, we extend it on uniform spaces.…”

Section: Definition 44 An Ifs T On a Uniform Space (T U) Is Called To...mentioning

confidence: 99%

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On Topological Shadowing and Chain Properties of IFS on Uniform Spaces

Devi¹,

Mangang²

2022

MJMS

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We define notions such as pseudo-orbit, topological shadowing, and topological chain transitivity of iterated function systems on compact uniform spaces. We prove that these notions are invariant under topological conjugacy on a compact uniform space. For an IFS on a compact uniform space with topological shadowing property, we show that the topological chain transitivity implies topological transitivity. We also show that in a connected compact uniform space, notions such as topological chain mixing, totally topological chain transitive, topological chain transitive, and topological chain recurrent are equivalent.

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Section: Topological Shadowing Property Of Iterated Function Systemsmentioning

confidence: 90%

Section: Theorem 44 Let T Be An Ifs On a Compact Uniform Space (T U) ...mentioning

confidence: 92%

Section: Preliminariesmentioning

confidence: 99%

Section: Definition 44 An Ifs T On a Uniform Space (T U) Is Called To...mentioning

confidence: 99%

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On Topological Shadowing and Chain Properties of IFS on Uniform Spaces

Devi¹,

Mangang²

2022

MJMS

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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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Chain Mixing and Chain Transitive Iterated Function Systems

Cited by 2 publications

References 10 publications

On Topological Shadowing and Chain Properties of IFS on Uniform Spaces

On Topological Shadowing and Chain Properties of IFS on Uniform Spaces

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

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Chain Mixing and Chain Transitive Iterated Function Systems

Cited by 2 publications

References 10 publications

On Topological Shadowing and Chain Properties of IFS on Uniform Spaces

On Topological Shadowing and Chain Properties of IFS on Uniform Spaces

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

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