Continuous orbit equivalence of semigroup actions

2021/09/27 by Qiang, Xiangqi, Hou, Chengjun
#Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2109.12831

Abstract

In this paper, we consider semigroup actions of discrete countable semigroups on compact spaces by surjective local homeomorphisms. We introduce notions of continuous one-sided orbit equivalence and continuous orbit equivalence for semigroup actions, and characterize them in terms of the corresponding semi-groupoids and transformation groupoids respectively. Finally, we consider the case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of group actions.

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