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

Tomoo Yokoyama

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

Dynamical Systems 2011-06-14 v3

Authors: Tomoo Yokoyama

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.

Keywords

Anosov diffeomorphism fixed points Smale conjecture stable foliation unstable foliation compact manifold

Cite

@article{arxiv.1106.1058,
  title  = {On a Smale Conjecture for the existence of fixed points for Anosov diffeomorphisms},
  author = {Tomoo Yokoyama},
  journal= {arXiv preprint arXiv:1106.1058},
  year   = {2011}
}

Comments

This paper has been withdrawn by the author due to a crucial error that the the constructed metric $g$ in the proof of the key lemma does not preserve subbundles

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