Some Criteria for Transitivity of Semigroup Actions
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DOI: 10.1007/s00009-018-1159-z
Abstract: In this paper, we study transitivity on the semigroup actions. Indeed, we introduce two criteria, “entropy minimality” and “nonuniformly expanding property”, to obtain transitivity. read more here.
Keywords: semigroup actions; criteria transitivity; transitivity semigroup;
A note on Poincaré recurrence for semigroup actions via Furstenberg family
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DOI: 10.1007/s00233-016-9828-3
Abstract: This paper presents an explanation of recurrence for semigroup actions from two points of view. The first one considers the concept of recurrence in the Poincaré sense as stated in Souza (Semigroup Forum 83:351–370, 2011)… read more here.
Keywords: recurrence; family; semigroup actions; recurrence semigroup ... See more keywords
Chaos, attraction, and control for semigroup actions
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DOI: 10.1007/s00233-020-10093-7
Abstract: This manuscript studies sensitivity and chaos for semigroup actions on completely regular spaces. The main results explain how the notions of attraction and control play a fundamental role in the investigation of Auslander–Yorke and Li–Yorke… read more here.
Keywords: semigroup actions; attraction control; control; chaos attraction ... See more keywords
Rates of Recurrence for Free Semigroup Actions
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DOI: 10.1007/s10883-020-09486-2
Abstract: We consider finitely generated free semigroup actions on (X, d) and generalize Boshernitzan’s quantitative recurrence theorem to general free semigroup actions. Let G be a finitely generated free semigroup endowed with a Bernoulli probability measure… read more here.
Keywords: free semigroup; semigroup; recurrence free; rates recurrence ... See more keywords
Polynomial Entropy of Subsets for Free Semigroup Actions
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DOI: 10.1007/s10883-021-09572-z
Abstract: In this paper, we introduce the notions of polynomial entropy on an arbitrary subset and lower local polynomial entropy for free semigroup actions. Also, we give some properties of Bowen polynomial entropy and discuss the… read more here.
Keywords: free semigroup; entropy; semigroup actions; bowen polynomial ... See more keywords
Entropy Points and Applications for Free Semigroup Actions
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DOI: 10.1007/s10955-021-02858-3
Abstract: The aim of this manuscript is to study some local properties of the topological entropy of a free semigroup action. In order to do that we focus on the set of entropy points of a… read more here.
Keywords: free semigroup; semigroup actions; points applications; applications free ... See more keywords
Some dynamical properties for free semigroup actions
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DOI: 10.1142/s0219493718500326
Abstract: In this paper, we introduce the notions of weakly mixing and totally transitivity for a free semigroup action. Let G be a free semigroup acting on a compact metric space generated by continuous open self-maps.… read more here.
Keywords: free semigroup; dynamical properties; semigroup; semigroup actions ... See more keywords
W-measurable sensitivity of semigroup actions
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DOI: 10.4064/cm7815-2-2020
Abstract: This paper studies the notion of W-measurable sensitivity in the context of semigroup actions. W-measurable sensitivity is a measurable generalization of sensitive dependence on initial conditions. In 2012, Grigoriev et. al. proved a classification result… read more here.
Keywords: semigroup; actions measurable; semigroup actions; measurable sensitivity ... See more keywords