Differentiable invariant manifolds of nilpotent parabolic points
Cufí Cabré, Clara (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Fontich, Ernest 1955- (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)

Date:	2021
Abstract:	We consider a map F of class Cr with a fixed point of parabolic type whose differential is not diagonalizable, and we study the existence and regularity of the invariant manifolds associated with the fixed point using the parameterization method. Concretely, we show that under suitable conditions on the coefficients of F, there exist invariant curves of class Cr away from the fixed point, and that they are analytic when F is analytic. The differentiability result is obtained as an application of the fiber contraction theorem. We also provide an algorithm to compute an approximation of a parameterization of the invariant curves and a normal form of the restricted dynamics of F on them.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00 Agencia Estatal de Investigación BES-2017-081570 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 Ministerio de Economía y Competitividad MTM2016-80117-P Agencia Estatal de Investigación PID2019-104851GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1374
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Parabolic point ; Invariant manifold ; Parameterization method
Published in:	Discrete and continuous dynamical systems. Series A, Vol. 41, Issue 10 (October 2021) , p. 4667-4704, ISSN 1553-5231

DOI: 10.3934/dcds.2021053

Postprint 43 p, 528.6 KB

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