Conjugacies and invariant manifolds via evolution semigroups

For a linear evolution family with a non-uniformly 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 non-autonomous non-uniformly hyperbolic dynamics to one that is autonomous and uniformly hyperbolic.Mathematics Subject Classification (2010): Primary: 37D99.Keywords: Conjugacies, evolution semigroups, invariant manifold