Publication
Abundance of elliptic dynamics on conservative three-flows
| dc.contributor.author | Bessa, Mário | |
| dc.contributor.author | Duarte, Pedro | |
| dc.date.accessioned | 2023-05-25T09:37:52Z | |
| dc.date.available | 2023-05-25T09:37:52Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | We consider a compact three-dimensional boundaryless Riemannian manifold M and the set of divergence-free (or zero divergence) vector fields without singularities, then we prove that this set has a C 1-residual (dense G_δ) such that any vector field inside it is Anosov or else its elliptical orbits are dense in the manifold M. This is the flow-setting counterpart of Newhouse's Theorem 1.3 (S. Newhouse, Quasi-elliptic periodic points in conservative dynamical systems, Am. J. Math. 99 (1977), pp. 1061–1087). Our result follows from two theorems, the first one says that if Λ is a hyperbolic invariant set for some class C^1 zero divergence vector field X on M, then either X is Anosov, or else Λ has empty interior. The second one says that, if X is not Anosov, then for any open set U ⊆ M there exists Y arbitrarily close to X such that Y t has an elliptical closed orbit through U. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | M. Bessa, P. Duarte, Abundance of elliptic dynamics on conservative three-flows, Dynamical Systems, 23, 4, 409-424, 2008 | pt_PT |
| dc.identifier.doi | 10.1080/14689360802162872 | pt_PT |
| dc.identifier.eissn | 1468–9375 | |
| dc.identifier.issn | 1468–9367 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/13833 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Taylor & Francis | pt_PT |
| dc.relation | ABUNDÂNCIA DE EXPOENTES DE IYAPUNOV ZERO EM SISTEMAS CONSERVATIVOS A TEMPO CONTÍNUO | |
| dc.relation.publisherversion | https://www.tandfonline.com/doi/abs/10.1080/14689360802162872 | pt_PT |
| dc.title | Abundance of elliptic dynamics on conservative three-flows | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | ABUNDÂNCIA DE EXPOENTES DE IYAPUNOV ZERO EM SISTEMAS CONSERVATIVOS A TEMPO CONTÍNUO | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/FARH/SFRH%2FBPD%2F20890%2F2004/PT | |
| oaire.citation.endPage | 424 | pt_PT |
| oaire.citation.issue | 4 | pt_PT |
| oaire.citation.startPage | 409 | pt_PT |
| oaire.citation.title | Dynamical Systems | pt_PT |
| oaire.citation.volume | 23 | pt_PT |
| oaire.fundingStream | FARH | |
| person.familyName | Bessa | |
| person.givenName | Mário | |
| person.identifier | https://scholar.google.com/citations?user=088yCR4AAAAJ&hl=pt-PT | |
| person.identifier.ciencia-id | C21A-EEC0-A3EF | |
| person.identifier.orcid | 0000-0002-1758-2225 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | restrictedAccess | pt_PT |
| rcaap.type | article | pt_PT |
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