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Title: On ergodicity of Markovian mostly expanding semi-group actions

Authors: A. Ehsani; F.H. Ghane; M. Zaj

Addresses: Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, 25529, Iran ' Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, 25529, Iran ' Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, 25529, Iran

Abstract: We consider finitely generated semigroup actions on a compact manifold and discuss their ergodic properties. We introduce Markovian mostly expanding semigroups and show that each C1+α Markovian mostly expanding semigroup action is ergodic (with respect to the Lebesgue measure) whenever it is strongly tranitive. Moreover, it is proved that each Markovian mostly expanding semigroup is non uniformly expanding. Our approach provides a large class of non-uniformly expanding semigroups.

Keywords: finitely generated semigroup action; backward minimality; strong transitivity; ergodicity of semigroup actions; non-uniformly expanding property.

DOI: 10.1504/IJDSDE.2020.104904

International Journal of Dynamical Systems and Differential Equations, 2020 Vol.10 No.1, pp.81 - 93

Received: 29 Dec 2017
Accepted: 12 Jul 2018

Published online: 05 Feb 2020 *

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