English

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

Dynamical Systems 2021-09-23 v2

Abstract

For every rN2{}r\in\mathbb{N}_{\geq2}\cup\{\infty\}, we prove the CrC^r-closing lemma for general and conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle. In particular, it implies periodic points are dense for CrC^r-generic conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle.

Keywords

Cite

@article{arxiv.2004.06855,
  title  = {$C^r$-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle},
  author = {Shaobo Gan and Yi Shi},
  journal= {arXiv preprint arXiv:2004.06855},
  year   = {2021}
}
R2 v1 2026-06-23T14:51:40.353Z