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arXiv · 2311.14433

SRB measures for mostly expanding partially hyperbolic diffeomorphisms via the variational approach

David Burguet·Dawei Yang
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Abstract

By using the variational approach, we prove the existence of Sinai-Ruelle-Bowen measures for partially hyperbolic $\mathcal C^1$ diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting $E\oplus F$, where $\dim E=1$ and $F$ is mostly expanding. When the diffeomorphisms are $\mathcal C^{1+\alpha}$, we prove the basin covering property for both cases.

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David Burguet, Dawei Yang. 2023-11-24. SRB measures for mostly expanding partially hyperbolic diffeomorphisms via the variational approach. https://arxiv.org/abs/2311.14433

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