Ergodic measures with large entropy have long unstable manifolds for C^∞ surface diffeomorphisms

2024/10/10 by Luo, Chiyi, Yang, Dawei · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.07979

Abstract

We prove that for ergodic measures with large entropy have long unstable manifolds for C^∞ surface diffeomorphisms. Specifically, for any α>0, there exist constants β>0 and c>0 such that for every ergodic measure μ with metric entropy large than α, the set of points with the size of unstable manifolds large than β has μ-measure large than c.

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