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arXiv · 1806.03089

On the stable ergodicity of diffeomorphisms with dominated splitting

Davi Obata
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Abstract

In this paper we obtain two criteria of stable ergodicity outside the partially hyperbolic scenario. In both criteria, we use a weak form of hyperbolicity called chain-hyperbolicity. It is obtained one criterion for diffeomorphisms with dominated splitting and one criterion for weakly partially hyperbolic diffeomorphisms. As an application of one of these criteria, we obtain the $C^1$-density of stable ergodicity inside a certain class of weakly partially hyperbolic diffeomorphisms.

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Davi Obata. 2018-06-08. On the stable ergodicity of diffeomorphisms with dominated splitting. https://doi.org/10.1088/1361-6544/aaea93

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