Quasi-Anosov diffeomorphisms and hyperbolic manifolds

Abstract

Let f be a diffeomorphism of a smooth manifold N and M ⊂ N M \subset N a compact boundaryless submanifold such that it is a hyperbolic set for f. The diffeomorphism f/M is characterized and it is proved that it is Anosov if and only if M is an invariant isolated set of f (i.e. the maximal invariant subset of some compact neighborhood). Isomorphisms of vector bundles with the property that the zero section is an isolated subset are studied proving that they can be embedded in hyperbolic vector bundle isomorphisms.