Rigidity of random group actions

Jung, WooChul; Lee, Keonhee; Morales, C. A.; Oh, Jumi

doi:10.3934/dcds.2020130

Discrete &Amp; Continuous Dynamical Systems - A

2020

DOI: 10.3934/dcds.2020130

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Rigidity of random group actions

WooChul Jung¹,

Keonhee Lee²,

C. A. Morales³

et al.

Abstract: We prove that if a finitely generated random group action is robustly expansive and has the shadowing property, then it is rigid. We apply this result to analyze the rigidity of certain iterated function systems or actions of the discrete Heisenberg group.

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Cited by 2 publications

References 16 publications

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Shadowable Points of Free Semigroup Actions

Li,

Ma,

Kuang

et al. 2024

Bull. Malays. Math. Sci. Soc.

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Shadowable Points of Free Semigroup Actions

Li,

Ma,

Kuang

et al. 2024

Bull. Malays. Math. Sci. Soc.

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Dynamic properties of random linear cocycles

Lee,

2023

Asian-European J. Math.

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In this paper, we extend the expansivity, pseudo trajectory tracing property and hyperbolicity of linear dynamical systems for the random view point. We show that to a random linear cocycle [Formula: see text] it is expansive if and only if it has the generalized pseudo trajectory tracing property. Moreover, we show that [Formula: see text] is topologically stable if and only if it is structurally stable.

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Rigidity of random group actions

Abstract: We prove that if a finitely generated random group action is robustly expansive and has the shadowing property, then it is rigid. We apply this result to analyze the rigidity of certain iterated function systems or actions of the discrete Heisenberg group.

Cited by 2 publications

References 16 publications

Shadowable Points of Free Semigroup Actions

Shadowable Points of Free Semigroup Actions

Dynamic properties of random linear cocycles

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