On ergodicity of mostly expanding semi-group actions

2015/05/13 by Azam Ehsani, Ehsani, Azam, Fatome-Helen Ghane +3
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1505.03367

openalex publication_date 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our results improve the main result in [8], where the ergodicity for one dimensional fiber was proved. We will introduce Markov partition for finitely generated semi-group actions and then we establish ergodicity for a large class of finitely generated semi-groups of C^1+alpha-diffeomorphisms that admit a Markov partition. Moreover, we present some transitivity criteria for semi-group actions and provide a weaker form of dynamical irreducibility that suffices to ergodicity in our setting.

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