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

Abstract

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

This paper has been withdrawn by the author due to a crucial error that the the constructed metric $g$ in the proof of the key lemma does not preserve subbundles