Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/20865

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.contributor	Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.contributor.author	Baldomá Barraca, Inmaculada
dc.contributor.author	Castejón i Company, Oriol
dc.contributor.author	Martínez-Seara Alonso, M. Teresa
dc.date	2013
dc.identifier.citation	Baldoma, I.; Castejon, O.; Martinez-seara, M. Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity. "Journal of dynamics and differential equations", 2013, vol. 25, núm. 2, p. 335-392.
dc.identifier.citation	1040-7294
dc.identifier.citation	10.1007/s10884-013-9297-2
dc.identifier.uri	http://hdl.handle.net/2117/20865
dc.language.iso	eng
dc.relation	http://link.springer.com/article/10.1007%2Fs10884-013-9297-2
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject	Perturbation (Mathematics)
dc.subject	Exponentially small phenomena
dc.subject	Splitting of separatrices
dc.subject	Hopf-zero singularity
dc.subject	Singular perturbation theory
dc.subject	Pertorbació (Matemàtica)
dc.title	Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	In this paper we prove the breakdown of a heteroclinic connection in the analytic versal unfoldings of the generic Hopf-zero singularity in an open set of the parameter space. 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 corresponding stable and unstable one-dimensional manifolds which is given by an exponentially small function in the perturbation parameter. Our result applies both for conservative and dissipative unfoldings
dc.description.abstract	Peer Reviewed

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