Please use this identifier to cite or link to this item:
Title: Invariant manifolds of parabolic fixed points (II). Approximations by sums of homogeneous functions.
Author: Baldomá, Inmaculada
Fontich, Ernest, 1955-
Martín, Pau
Keywords: Sistemes dinàmics diferenciables
Teoria ergòdica
Anàlisi numèrica
Geometria hiperbòlica
Differentiable dynamical systems
Ergodic theory
Numerical analysis
Hyperbolic geometry
Issue Date: 15-Apr-2020
Publisher: Elsevier
Abstract: We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible to obtain polynomial approximations. Here we develop an algorithm to obtain them as sums of homogeneous functions by solving suitable cohomological equations. We deal with both the differentiable and analytic cases. We also study the dependence on parameters. In the companion paper [BFM] these approximations are used to obtain the existence of true invariant manifolds close by. Examples are provided.
Note: Versió postprint del document publicat a:
It is part of: Journal of Differential Equations, 2020, vol. 268, num. 9, p. 5574-5627
Related resource:
ISSN: 0022-0396
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

Files in This Item:
File Description SizeFormat 
699369.pdf585.37 kBAdobe PDFView/Open

This item is licensed under a Creative Commons License Creative Commons