The role of the saddle-foci on the structure of a bykov attracting set

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorBessa, Mário-
Autor(es): dc.creatorCarvalho, Maria-
Autor(es): dc.creatorRodrigues, Alexandre A. P.-
Data de aceite: dc.date.accessioned2025-08-22T11:53:33Z-
Data de disponibilização: dc.date.available2025-08-22T11:53:33Z-
Data de envio: dc.date.issued2023-05-30-
Data de envio: dc.date.issued2023-05-30-
Data de envio: dc.date.issued2019-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/10400.2/13896-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/10400.2/13896-
Descrição: dc.descriptionWe consider a one-parameter family ( fλ)λ 􏰅 0 of symmetric vector fields on the three-dimensional sphere whose flows exhibit a heteroclinic network between two saddle-foci inside a global attracting set. More precisely, when λ = 0, there is an attracting heteroclinic cycle between the two equilibria which is made of two 1- dimensional connections together with a 2-dimensional sphere which is both the stable manifold of one saddle-focus and the unstable manifold of the other. After slightly increasing the parameter while keeping the 1-dimensional connections unaltered, the two-dimensional invariant manifolds of the equilibria become transversal, and thereby create homoclinic and heteroclinic tangles. It is known that these newborn structures are the source of a countable union of topological horseshoes, which prompt the coexistence of infinitely many sinks and saddle-type invariant sets for many values of λ. We show that, for every small enough positive parameter λ, the stable and unstable manifolds of the saddle-foci and those infinitely many horseshoes are contained in the global attracting set of fλ; moreover, the horseshoes belong to the heteroclinic class of the equilibria. In addition, we show that the set of chain-accessible points from either of the saddle-foci is chain-stable and contains the closure of the invariant manifolds of the two equilibria.-
Descrição: dc.descriptioninfo:eu-repo/semantics/publishedVersion-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Publicador: dc.publisherSpringer-
Relação: dc.relationCentre for Mathematics of the University of Porto-
Relação: dc.relationHeteroclinic dynamics: beyond intermittency-
Relação: dc.relationhttps://link.springer.com/article/10.1007/s12346-020-00373-6-
Palavras-chave: dc.subjectHeteroclinic cycle-
Palavras-chave: dc.subjectBykov network-
Palavras-chave: dc.subjectChain-accessible-
Palavras-chave: dc.subjectChain-recurrent-
Palavras-chave: dc.subjectSymmetry-
Título: dc.titleThe role of the saddle-foci on the structure of a bykov attracting set-
Aparece nas coleções:Repositório Aberto - Universidade Aberta (Portugal)

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