A quasi-anosov diffeomorphism that is not anosov(1)

In this note, we give an example of a diffeomorphism ƒ on a three dimensional manifold M such that ƒ has a property called quasi-Anosov but such that ƒ does not have a hyperbolic structure (is not Anosov). Mane has given a method of extending ƒ 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.