arXiv 1505.033672015-05-13math.DS

关于大多扩张半群作用的遍历性

On ergodicity of mostly expanding semi-group actions

Azam Ehsani, Fatome-Helen Ghane, Marzie Zaj

摘要：

本文研究了m维闭流形M上光滑生成半群的光滑作用的遍历性。我们提供了关于勒贝格测度遍历的作用的充分条件。我们的结果改进了文[8]中的主要结果，其中证明了一维纤维的遍历性。我们将对C^{1+ alpha}-群同态的半生成群作用引入马尔可夫划分，然后建立了一大类C^{1+alpha}-群同态的半生成半群的遍历性，这类半群允许一个马尔可夫分割.此外，我们给出了半群作用的传递性准则，并给出了一个较弱形式的动力学不可约性，在我们的设置，足以遍历。

英文摘要：

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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