Local stable and unstable manifolds for Anosov families

Abstract

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. They are time-dependent dynamical systems with hyperbolic behavior. In addition to presenting several properties and examples of Anosov families, in this paper we build local stable and local manifolds for such families.