{"paper":{"title":"Multiple brake orbits in $\\mathbf m$-dimensional disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. Giannoni, P. Piccione, R. Giamb\\`o","submitted_at":"2015-03-19T15:39:24Z","abstract_excerpt":"Let $(M,g)$ be a (complete) Riemannian surface, and let $\\Omega\\subset M$ be an open subset whose closure is homeomorphic to a disk. We prove that if $\\partial\\Omega$ is smooth and it satisfies a strong concavity assumption, then there are at least two distinct orthogonal geodesics in $\\overline\\Omega=\\Omega \\bigcup\\partial\\Omega$. Using the results given in [6], we then obtain a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. In our proof we shall use recent deformation results proved in [7]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05805","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"}