arXiv Analytics

Sign in

arXiv:1011.2844 [math.DS]AbstractReferencesReviewsResources

A diffeomorphism with global dominated splitting can not be minimal

Pengfei Zhang

Published 2010-11-12Version 1

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.

Comments: 5 pages. An application of Liao's selecting lemma
Categories: math.DS
Subjects: 37D30
Related articles: Most relevant | Search more
arXiv:0912.2699 [math.DS] (Published 2009-12-14, updated 2010-05-04)
Nonuniform Hyperbolicity, Global Dominated Splittings and Generic Properties of Volume-Preserving Diffeomorphisms
arXiv:0809.3309 [math.DS] (Published 2008-09-19)
Nonuniform hyperbolicity for C^1-generic diffeomorphisms
arXiv:2405.11366 [math.DS] (Published 2024-05-18)
All, most, some? On diffeomorphisms of the interval that are distorted and/or conjugate to powers of themselves

Links

Toolbox