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Breakdown of heteroclinic orbits for analytic unfoldings of the hopf-zero singularity. The singular case

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Baldomá Barraca, InmaculadaMés informacióMés informacióMés informació
Castejón i Company, Oriol
Martínez-Seara Alonso, M. TeresaMés informacióMés informacióMés informació
Document typeResearch report
Defense date2011
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 an heteroclinic connection in the analytic versal unfoldings of the generic Hopf-Zero singularity. This heteroclinic orbit appears at any order if one performs the normal form around the origin, therefore it is a phenomenon \beyond all orders". In this paper we provide a formula for the distance between the correspond- ing stable and unstable one dimensional manifolds which is given by an exponentially small function in the perturbation parameter. Our result applies both for conservative unfoldings and for dissipative ones in some open regions of the parameter plane
CitationBaldomá, I.; Castejón, O.; Martínez-Seara, M. "Breakdown of heteroclinic orbits for analytic unfoldings of the hopf-zero singularity. The singular case". 2011. 
URIhttp://hdl.handle.net/2117/15085
URL other repositoryhttp://www.ma1.upc.edu/recerca/preprints/2011/
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