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arXiv · 1804.03328

On the abundance of SRB measures

Yongluo Cao·Zeya Mi·Dawei Yang
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Abstract

We prove the abundance of Sinai-Ruelle-Bowen measures for diffeomorphisms away from ones with a homoclinic tangency. This is motivated by conjectures of Palis on the existence of physical (Sinai-Ruelle-Bowen) measures for global dynamics. The main novelty in this paper is that we have to deeply study Gibbs $cu$-states in different levels. Note that we have to use random perturbations to give some upper bound of the level of Gibbs $cu$-states.

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Yongluo Cao, Zeya Mi, Dawei Yang. 2018-04-10. On the abundance of SRB measures. https://arxiv.org/abs/1804.03328

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