Diffeomorphisms with global dominated splittings cannot be minimal

Zhang, Pengfei

doi:10.1090/S0002-9939-2011-10956-0

Diffeomorphisms with global dominated splittings cannot be minimal
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Proc. Amer. Math. Soc. 140 (2012), 589-593 Request permission

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 $f$ cannot be minimal. The proof mainly uses Mañé’s argument and Liao’s selecting lemma.

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