On ergodicity of Markovian mostly expanding semi-group actions

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.