Publication
On the stability of the set of hyperbolic closed orbits of a hamiltonian
| dc.contributor.author | Bessa, Mário | |
| dc.contributor.author | Ferreira, Celia | |
| dc.contributor.author | Rocha, Jorge | |
| dc.date.accessioned | 2023-05-26T10:38:03Z | |
| dc.date.available | 2023-05-26T10:38:03Z | |
| dc.date.issued | 2009-09-21 | |
| dc.description.abstract | A Hamiltonian level, say a pair $(H,e)$ of a Hamiltonian $H$ and an energy $e \in \mathbb{R}$, is said to be Anosov if there exists a connected component $\mathcal{E}_{H,e}$ of $H^{-1}({e})$ which is uniformly hyperbolic for the Hamiltonian flow $X_H^t$. The pair $(H,e)$ is said to be a Hamiltonian star system if there exists a connected component $\mathcal{E}^\star_{H,e}$ of the energy level $H^{-1}({{e}})$ such that all the closed orbits and all the critical points of $\mathcal{E}^\star_{H,e}$ are hyperbolic, and the same holds for a connected component of the energy level $\tilde{H}^{-1}({\tilde{e}})$, close to $\mathcal{E}^\star_{H,e}$, for any Hamiltonian $\tilde{H}$, in some $C^2$-neighbourhood of $H$, and $\tilde{e}$ in some neighbourhood of $e$. In this article we prove that for any four-dimensional Hamiltonian star level $(H,e)$ if the surface $\mathcal{E}^\star_{H,e}$ does not contain critical points, then $X_H^t|_{\mathcal{E}^\star_{H,e}}$ is Anosov; if $\mathcal{E}^\star_{H,e}$ has critical points, then there exists $\tilde{e}$, arbitrarily close to $e$, such that $X_H^t|_{\mathcal{E}^\star_{H,\tilde{e}}}$ is Anosov. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | M. Bessa, C. Ferreira, J. Rocha, On the Stability of the Set of Hyperbolic Closed Orbits of a Hamiltonian, Mathematical Proceedings of the Cambridge Philosophical Society, 149, 2, 373-383, 2009 | pt_PT |
| dc.identifier.doi | 10.1017/S0305004110000253 | pt_PT |
| dc.identifier.uri | http://hdl.handle.net/10400.2/13862 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Cambridge University Press | pt_PT |
| dc.relation | ABUNDÂNCIA DE EXPOENTES DE IYAPUNOV ZERO EM SISTEMAS CONSERVATIVOS A TEMPO CONTÍNUO | |
| dc.relation | PROGRAMA INTER-UNIVERSITÁRIO DE DOUTORAMENTO EM MATEMÁTICA | |
| dc.title | On the stability of the set of hyperbolic closed orbits of a hamiltonian | 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.awardTitle | PROGRAMA INTER-UNIVERSITÁRIO DE DOUTORAMENTO EM MATEMÁTICA | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/FARH/SFRH%2FBPD%2F20890%2F2004/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/PIDDAC/SFRH%2FBD%2F33100%2F2007/PT | |
| oaire.citation.endPage | 383 | pt_PT |
| oaire.citation.issue | 2 | pt_PT |
| oaire.citation.startPage | 373 | pt_PT |
| oaire.citation.title | Mathematical Proceedings of the Cambridge Philosophical Society | pt_PT |
| oaire.citation.volume | 149 | pt_PT |
| oaire.fundingStream | FARH | |
| oaire.fundingStream | PIDDAC | |
| 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.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 | |
| rcaap.rights | restrictedAccess | pt_PT |
| rcaap.type | article | pt_PT |
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