English

A diffeomorphism with global dominated splitting can not be minimal

Dynamical Systems 2024-04-02 v1

Abstract

Let M be a closed manifold and f be a diffeomorphism on M. We show that if f has a nontrivial dominated splitting TM=E\oplus F, then f can not be minimal. The proof mainly use Mane's argument and Liao's selecting lemma.

Keywords

Cite

@article{arxiv.1011.2844,
  title  = {A diffeomorphism with global dominated splitting can not be minimal},
  author = {Pengfei Zhang},
  journal= {arXiv preprint arXiv:1011.2844},
  year   = {2024}
}

Comments

5 pages. An application of Liao's selecting lemma

R2 v1 2026-06-21T16:42:45.910Z