On the stability of the set of hyperbolic closed orbits of a hamiltonian

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorBessa, Mário-
Autor(es): dc.creatorFerreira, Célia-
Autor(es): dc.creatorRocha, Jorge-
Data de aceite: dc.date.accessioned2025-08-21T15:22:37Z-
Data de disponibilização: dc.date.available2025-08-21T15:22:37Z-
Data de envio: dc.date.issued2023-05-26-
Data de envio: dc.date.issued2023-05-26-
Data de envio: dc.date.issued2009-09-21-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/10400.2/13862-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/10400.2/13862-
Descrição: dc.descriptionA 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.-
Descrição: dc.descriptioninfo:eu-repo/semantics/publishedVersion-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Publicador: dc.publisherCambridge University Press-
Relação: dc.relationABUNDÂNCIA DE EXPOENTES DE IYAPUNOV ZERO EM SISTEMAS CONSERVATIVOS A TEMPO CONTÍNUO-
Relação: dc.relationPROGRAMA INTER-UNIVERSITÁRIO DE DOUTORAMENTO EM MATEMÁTICA-
Título: dc.titleOn the stability of the set of hyperbolic closed orbits of a hamiltonian-
Aparece nas coleções:Repositório Aberto - Universidade Aberta (Portugal)

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