Publication
The role of the saddle-foci on the structure of a bykov attracting set
| dc.contributor.author | Bessa, Mário | |
| dc.contributor.author | Carvalho, Maria | |
| dc.contributor.author | Rodrigues, Alexandre A. P. | |
| dc.date.accessioned | 2023-05-30T10:12:04Z | |
| dc.date.available | 2023-05-30T10:12:04Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | We 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. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | Bessa, M., Carvalho, M. & Rodrigues, A.A.P. The Role of the Saddle-Foci on the Structure of a Bykov Attracting Set. Qual. Theory Dyn. Syst. 19, 29 (2020) | pt_PT |
| dc.identifier.doi | 10.1007/s12346-020-00373-6 | pt_PT |
| dc.identifier.uri | http://hdl.handle.net/10400.2/13896 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Springer | pt_PT |
| dc.relation | Centre for Mathematics of the University of Porto | |
| dc.relation | Heteroclinic dynamics: beyond intermittency | |
| dc.relation.publisherversion | https://link.springer.com/article/10.1007/s12346-020-00373-6 | pt_PT |
| dc.subject | Heteroclinic cycle | pt_PT |
| dc.subject | Bykov network | pt_PT |
| dc.subject | Chain-accessible | pt_PT |
| dc.subject | Chain-recurrent | pt_PT |
| dc.subject | Symmetry | pt_PT |
| dc.title | The role of the saddle-foci on the structure of a bykov attracting set | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Centre for Mathematics of the University of Porto | |
| oaire.awardTitle | Heteroclinic dynamics: beyond intermittency | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F29126%2F2017/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F00144%2F2019/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/Investigador FCT/IF%2F00107%2F2015%2FCP1286%2FCT0001/PT | |
| oaire.citation.issue | 1 | pt_PT |
| oaire.citation.title | Qualitative Theory of Dynamical Systems | pt_PT |
| oaire.citation.volume | 19 | pt_PT |
| oaire.fundingStream | 3599-PPCDT | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | Investigador FCT | |
| person.familyName | Bessa | |
| person.familyName | Carvalho | |
| person.familyName | Rodrigues | |
| person.givenName | Mário | |
| person.givenName | Maria | |
| person.givenName | Alexandre | |
| person.identifier | https://scholar.google.com/citations?user=088yCR4AAAAJ&hl=pt-PT | |
| person.identifier.ciencia-id | C21A-EEC0-A3EF | |
| person.identifier.ciencia-id | 361B-4DA8-0A98 | |
| person.identifier.ciencia-id | 7C15-AD8C-4AA7 | |
| person.identifier.orcid | 0000-0002-1758-2225 | |
| person.identifier.orcid | 0000-0001-6929-6442 | |
| person.identifier.orcid | 0000-0001-8182-9889 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
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