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Breakdown of a 2D heteroclinic connection in the hopf-zero singularity (I)

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Baldomá Barraca, InmaculadaMés informacióMés informacióMés informació
Castejón Company, Oriol
Martínez-Seara Alonso, M. TeresaMés informacióMés informacióMés informació
Document typeArticle
Defense date2018-10-01
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
In this paper we study a beyond all orders phenomenon which appears in the analytic unfoldings of the Hopf-zero singularity. It consists in the breakdown of a two-dimensional heteroclinic surface which exists in the truncated normal form of this singularity at any order. The results in this paper are twofold: on the one hand, we give results for generic unfoldings which lead to sharp exponentially small upper bounds of the difference between these manifolds. On the other hand, we provide asymptotic formulas for this difference by means of the Melnikov function for some non-generic unfoldings.
CitationBaldoma, I.; Castejón, O.; Martinez-seara, T. Breakdown of a 2D heteroclinic connection in the hopf-zero singularity (I). "Journal of nonlinear science", 1 Octubre 2018, vol. 28, núm. 5, p. 1551-1627. 
URIhttp://hdl.handle.net/2117/133743
DOI10.1007/s00332-018-9458-x
ISSN0938-8974
Publisher versionhttps://link.springer.com/article/10.1007/s00332-018-9458-x
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