On the abundance of SRB measures

2018/04/10 by Yongluo Cao, Cao, Yongluo, Zeya Mi +3 · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1804.03328

openalex publication_date 2018/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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