Conjugacies and invariant manifolds via evolution semigroups

Abstract

For a linear evolution family with a nonuniformly hyperbolic behavior, we give simple proofs of the existence of topological conjugacies and stable invariant manifolds under sufficiently small perturbations. The proofs are obtained via evolution semigroups, which allows us to pass from the original nonautonomous nonuni-formly hyperbolic dynamics to one that is autonomous and uniformly hyperbolic.