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2020-04-15

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cc-by-nc-nd (c) Elsevier, 2020
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/193550

Invariant manifolds of parabolic fixed points (II). Approximations by sums of homogeneous functions.

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https://doi.org/10.1016/j.jde.2019.11.099

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.

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Sistemes dinàmics diferenciables, Teoria ergòdica, Anàlisi numèrica, Geometria hiperbòlica

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Differentiable dynamical systems, Ergodic theory, Numerical analysis, Hyperbolic geometry

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Articles publicats en revistes (Matemàtiques i Informàtica)

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BALDOMÁ, Inmaculada, FONTICH, Ernest and MARTÍN, Pau. Invariant manifolds of parabolic fixed points (II). Approximations by sums of homogeneous functions. Journal of Differential Equations. 2020. Vol. 268, num. 9, pags. 5574-5627. ISSN 0022-0396. [consulted: 13 of June of 2026]. Available at: https://hdl.handle.net/2445/193550

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