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arXiv · 2410.07979

Ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms

Chiyi Luo·Dawei Yang
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Abstract

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

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Chiyi Luo, Dawei Yang. 2024-10-10. Ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms. https://doi.org/10.1007/s00023-026-01679-y

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