$C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle

Shaobo Gan; Yi Shi

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arXiv · 2004.06855

$C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle

Shaobo Gan·Yi Shi

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Abstract

For every $r\in\mathbb{N}_{\geq2}\cup\{\infty\}$, we prove the $C^r$-closing lemma for general and conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle. In particular, it implies periodic points are dense for $C^r$-generic conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle.

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Shaobo Gan, Yi Shi. 2020-04-15. $C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle. https://arxiv.org/abs/2004.06855

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