Manifolds – Optimal Regularity for Nonuniformly Hyperbolic Dynamics
نویسندگان
چکیده
For sufficiently 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 fiber contraction principle to establish the regularity property. We note that the argument also applies to sufficiently small linear perturbations, without further changes.
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