Finiteness of physical measures for diffeomorphisms with multi 1-D centers

Yongluo Cao; Zeya Mi

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arXiv · 2306.06575

Finiteness of physical measures for diffeomorphisms with multi 1-D centers

Yongluo Cao·Zeya Mi

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Abstract

Let $f$ be a $C^2$ diffeomorphism on compact Riemannian manifold $M$ with partially hyperbolic splitting $$ TM=E^u\oplus E_1^c\oplus\cdots\oplus E_k^c \oplus E^s, $$ where $E^u$ is uniformly expanding, $E^s$ is uniformly contracting, and ${\rm dim}E_i^c=1,~ 1\le i \le k, ~k\ge 1$. We prove the finiteness of ergodic physical(SRB) measures of $f$ under the hyperbolicity of Gibbs $u$-states.

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Yongluo Cao, Zeya Mi. 2023-06-11. Finiteness of physical measures for diffeomorphisms with multi 1-D centers. https://arxiv.org/abs/2306.06575

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