Center Manifolds Optimal Regularity for Nonuniformly Hyperbolic Dynamics

Abstract

For suciently small perturbations with continuous deriva- tive, 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 exponen- tial behavior as a very special case. Our proof uses the ber contraction principle to establish the regularity property. We note that the argu- ment also applies to suciently small linear perturbations, without further changes.