{"paper":{"title":"On the Stability of the Set of Hyperbolic Closed Orbits of a Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Celia Ferreira, Jorge Rocha, Mario Bessa","submitted_at":"2009-09-21T15:29:45Z","abstract_excerpt":"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}({\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3801","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}