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arXiv · 2308.00297

A volume preserving nonuniformly hyperbolic diffeomorphism with arbitrary number of ergodic components and close to the identity

Jianyu Chen·Huyi Hu·Yun Yang
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Abstract

We prove that for any $\ell\in\NN\cup\{\infty\}$ and any $r\in \NN$, every compact smooth Riemannian manifold $\cM$ of $\dim \cM\ge 5$ carries a $C^\infty$ volume preserving nonuniformly hyperbolic diffeomorphism, which has exactly $\ell$ ergodic components (in fact, Bernoulli components) and is $C^r$ close to the identity.

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Jianyu Chen, Huyi Hu, Yun Yang. 2023-08-01. A volume preserving nonuniformly hyperbolic diffeomorphism with arbitrary number of ergodic components and close to the identity. https://arxiv.org/abs/2308.00297

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