dc.contributor.author
Baldomá, Inmaculada
dc.contributor.author
Fontich, Ernest, 1955-
dc.contributor.author
Martín, Pau
dc.date.issued
2023-02-13T19:37:16Z
dc.date.issued
2023-02-13T19:37:16Z
dc.date.issued
2020-04-15
dc.date.issued
2023-02-13T19:37:16Z
dc.identifier
https://hdl.handle.net/2445/193550
dc.description.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.
dc.format
application/pdf
dc.relation
Versió postprint del document publicat a: https://doi.org/10.1016/j.jde.2019.11.099
dc.relation
Journal of Differential Equations, 2020, vol. 268, num. 9, p. 5574-5627
dc.relation
https://doi.org/10.1016/j.jde.2019.11.099
dc.rights
cc-by-nc-nd (c) Elsevier, 2020
dc.rights
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights
info:eu-repo/semantics/openAccess
dc.source
Articles publicats en revistes (Matemàtiques i Informàtica)
dc.subject
Sistemes dinàmics diferenciables
dc.subject
Teoria ergòdica
dc.subject
Anàlisi numèrica
dc.subject
Geometria hiperbòlica
dc.subject
Differentiable dynamical systems
dc.subject
Ergodic theory
dc.subject
Numerical analysis
dc.subject
Hyperbolic geometry
dc.title
Invariant manifolds of parabolic fixed points (II). Approximations by sums of homogeneous functions.
dc.type
info:eu-repo/semantics/article
dc.type
info:eu-repo/semantics/acceptedVersion
