Existence of conjugacies and stable manifolds via suspensions

Abstract

We obtain in a simpler manner versions of the Grobman-Hartman theorem and of the stable manifold theorem for a sequence of maps on a Banach space, which corresponds to consider a nonautonomous dynamics with discrete time. The proofs are made short by using a suspension to an infinite-dimensional space that makes the dynamics autonomous (and uniformly hyperbolic when originally it was nonuniformly hyperbolic).

Keywords

• Conjugacies
• nonuniform hyperbolicity
• stable manifolds