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Title: Invariant manifolds of parabolic fixed points (I). Existence and dependence on parameters.
Author: Baldomá, Inmaculada
Fontich, Ernest, 1955-
Martín, Pau
Keywords: Sistemes dinàmics hiperbòlics
Teoria ergòdica
Equacions diferencials ordinàries
Anàlisi numèrica
Hyperbolic dynamical systems
Ergodic theory
Ordinary differential equations
Numerical analysis
Issue Date: 15-Apr-2020
Publisher: Elsevier
Abstract: Abstract. In this paper we study the existence and regularity of stable manifolds associated to fixed points of parabolic type in the differentiable and analytic cases, using the parametrization method. The parametrization method relies on a suitable approximate solution of a functional equation. In the case of parabolic points, if the manifolds have dimension two or higher, in general this approximation cannot be obtained in the ring of polynomials but as a sum of homogeneous functions and it is given in [BFM]. Assuming a sufficiently good approximation is found, here we provide an "a posteriori" result which gives a true invariant manifold close to the approximated one. In the differentiable case, in some cases, there is a loss of regularity. We also consider the case of parabolic periodic orbits of periodic vector fields and the dependence of the manifolds on parameters. Examples are provided. We apply our method to prove that in several situations, namely, related to the parabolic infinity in the elliptic spatial three body problem, these invariant manifolds exist and do have polynomial approximations.
Note: Versió postprint del document publicat a:
It is part of: Journal of Differential Equations, 2020, vol. 268, num. 9, p. 5516-5573
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ISSN: 0022-0396
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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