Center Manifolds Optimal Regularity for Nonuniformly Hyperbolic Dynamics

Abstract

For suciently small perturbations with continuous derivative, we show how to establish the optimal regularity of invariant center manifolds when the linear equation admits a nonuniform exponential trichotomy. We also consider the general case of exponential growth rates given by an arbitrary function. This includes the usual exponential behavior as a very special case. Our proof uses the ber contraction principle to establish the regularity property. We note that the argument also applies to sufficiently small linear perturbations, without further changes.