On a Smale Conjecture for the existence of fixed points for Anosov diffeomorphisms

preprint2011arXivOpen access

Abstract

We prove that if the stable foliation and the unstable foliation of an Anosov diffeomorphism on a connected compact manifold are C3C^3, then the diffeomorphism has fixed points. This is a partial positive answer to a Smale conjecture for fixed points of Anosov diffeomorphisms.

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