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Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II): The generic case

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Baldomá Barraca, InmaculadaMés informacióMés informacióMés informació
Castejón Company, Oriol
Martínez-Seara Alonso, M. TeresaMés informacióMés informacióMés informació
Document typeArticle
Defense date2018-04-17
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
In this paper, we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singularity. The method consists in obtaining an asymptotic formula for the difference between these manifolds which turns to be exponentially small respect to the unfolding parameter. The formula obtained is explicit but depends on the so-called Stokes constants, which arise in the study of the original vector field and which corresponds to the so-called inner equation in singular perturbation theory.
CitationBaldoma, I.; Castejón, O.; Martinez-seara, T. Breakdown of a 2D heteroclinic connection in the Hopf-zero singularity (II): The generic case. "Journal of nonlinear science", 17 Abril 2018, vol. 28, núm. 4, p. 1489-1549. 
URIhttp://hdl.handle.net/2117/133744
DOI10.1007/s00332-018-9459-9
ISSN0938-8974
Publisher versionhttps://link.springer.com/article/10.1007%2Fs00332-018-9459-9
Other identifiershttps://mat-web.upc.edu/people/tere.m-seara/articles/BaldomaCSJNLS2018_II.pdf
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