Openness of the Anosov families

Jeovanny de Jesus Muentes Acevedo

Published 2017-09-02Version 1

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a sequence of diffeomorphisms whit similar behavior to an Anosov diffeomorphisms. The set consisting of families of diffeomorphisms is equipped with the strong topology (or Whitney topology). We show that the set consisting of Anosov families is an open subset of the families of diffeomorphisms.