Gevrey asymptotic properties of slow manifolds. (2nd December 2019)

• Record Type: Journal Article
• Authors: De Maesschalck, Peter; Kenens, Karel
• Is Part Of: Nonlinearity. Volume 33:Number 1(2020)
• Page Start: 341
• Page End: 387
• Publication Date: 2019-12-02
• Subjects: slow-fast systems -- Gevrey asymptotics -- Borel summability -- singular perturbations -- slow manifolds -- elliptic manifolds; 34E15 -- 34M25 -- 34M30; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab4d86
• Languages: English
• ISSNs: 0951-7715

Abstract

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, Gevrey-asymptotics, and studies in the Borel plane.