A quasi-Anosov diffeomorphism that is not Anosov

Abstract

In this note, we give an example of a diffeomorphism f on a three dimensional manifold M such that f has a property called quasi- Anosov but such that f does not have a hyperbolic structure (is not Anosov). Mañé has given a method of extending f to a diffeomorphism g on a larger dimensional manifold V such that g has a hyperbolic structure on M as a subset of V. This gives a counterexample to a question of M. Hirsch.