Rates of Recurrence for Free Semigroup Actions

Liang, Yao; Zhao, Chuanwen

doi:10.1007/s10883-020-09486-2

Cited by 2 publications

(1 citation statement)

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“…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. For more recent results on finitely generated group or semigroup actions on compact metric spaces, we refer the reader to [7,10,12,15,23,30] and references therein.…”

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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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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Clifford semigroup actions

Paul

Maity

2022

Asian-European J. Math.

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In this paper, we establish the orbit-stabilizer theorem and the orbit decomposition theorem for a Clifford semigroup. Moreover, we establish that for a Clifford semigroup [Formula: see text], any two homogeneous Clifford [Formula: see text]-sets [Formula: see text] and [Formula: see text] are Clifford [Formula: see text]-isomorphic if and only if for any [Formula: see text], [Formula: see text] is conjugate to [Formula: see text]. More generally, for a Clifford semigroup [Formula: see text], any two Clifford [Formula: see text]-sets [Formula: see text] and [Formula: see text] are Clifford [Formula: see text]-isomorphic if and only if there is a bijection [Formula: see text] satisfying the property that, for all [Formula: see text], [Formula: see text] is Clifford [Formula: see text]-isomorphic to [Formula: see text]. Finally, we prove that in a Clifford semigroup [Formula: see text], for any element [Formula: see text] such that [Formula: see text] is [Formula: see text]-unitary full Clifford subsemigroup of [Formula: see text], [Formula: see text], where [Formula: see text] is the conjugacy class in [Formula: see text] containing the element [Formula: see text].

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Rates of Recurrence for Free Semigroup Actions

Cited by 2 publications

References 11 publications

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

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

Clifford semigroup actions

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