Gevrey asymptotic properties of slow manifolds

Abstract

In geometric singular perturbation theory, Fenichel manifolds are typically only finitely smooth. In this paper, we prove better local smoothness properties in the analytic setting, under the condition that no singularities in the slow flow are present. We also investigate cases where the slow flow has a node or focus, where summability results are obtained. Various techniques are being employed like formal power series methods, majorant equations, Gevreyasymptotics, and studies in the Borel plane.