Hyperbolic cones for casual diffeomorphisms

Abstract

Abstract This paper begins with introducing a new class of diffeomorphisms on pseudo-Riemannian manifolds which are called casual diffeomorphisms. We deduce a new pseudo-Riemannian metric via a casual diffeomorphism. We introduce a class of cones for a diffeomorphism, and we prove the existence of such cones for each p in a hyperbolic set of a casual diffeomorphism. As an example we find a hyperbolic casual diffeomorphism on a Schwarzschild pseudo-Riemannian manifold, and show that the whole manifold is a hyperbolic set for it.