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Gevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed points

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Baldomá Barraca, InmaculadaMés informacióMés informacióMés informació
Fontich, Ernest
Martín, Pau
Document typeArticle
Defense date2017-08-01
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
We study the Gevrey character of a natural parameterization of one dimensional invariant manifolds associated to a parabolic direction of fixed points of analytic maps, that is, a direction associated with an eigenvalue equal to 1. We show that, under general hypotheses, these invariant manifolds are Gevrey with type related to some explicit constants. We provide examples of the optimality of our results as well as some applications to celestial mechanics, namely, the Sitnikov problem and the restricted planar three body problem.
CitationBaldoma, I., Fontich, E., Martín, P. Gevrey estimates for one dimensional parabolic invariant manifolds of non-hyperbolic fixed points. "Discrete and continuous dynamical systems. Series A", 1 Agost 2017, vol. 37, núm. 8, p. 4159-4190. 
URIhttp://hdl.handle.net/2117/105920
DOI10.3934/dcds.2017177
ISSN1078-0947
Publisher versionhttp://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=14028
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