Equicontinuity and sensitivity on countable amenable semigroup

Authors: NADER ASADI KARAM, MOHAMMAD KBARI TOOTKABONI, ABBAS SAHLEH

Abstract: In this paper, we obtain the classification of topological dynamical systems with a discrete action. The equicontinuity and sensitivity for amenable discrete countable semigroup action are shown by the left Følner sequence. We consider the notion of uniquely ergodic and mean equicontinuous on amenable discrete countable semigroup action and develop the notion of density with respect to the Følner sequence on equicontinuous and sensitivity.

Keywords: Measure-preserving dynamical system, semigroup action, equicontinuity, sensitivity, amenable semigroup, Følner sequence, density

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