A diffeomorphism with global dominated splitting can not be minimal
arXiv:1011.2844 · doi:10.1090/S0002-9939-2011-10956-0
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.
5 pages. An application of Liao's selecting lemma