{"paper":{"title":"Tonelli Hamiltonians without conjugate points and $C^0$ integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.DS","authors_text":"Marc Arcostanzo, Marie-Claude Arnaud, Maxime Zavidovique, Philippe Bolle","submitted_at":"2013-09-24T08:19:50Z","abstract_excerpt":"We prove that all the Tonelli Hamiltonians defined on the cotangent bundle $T^*\\T^n$ of the $n$-dimensional torus that have no conjugate points are $C^0$ integrable, i.e. $T^*\\T^n$ is $C^0$ foliated by a family $\\Fc$ of invariant $C^0$ Lagrangian graphs. Assuming that the Hamiltonian is $C^\\infty$, we prove that there exists a $G_\\delta$ subset $\\Gc$ of $\\Fc$ such that the dynamics restricted to every element of $\\Gc$ is strictly ergodic. Moreover, we prove that the Lyapunov exponents of every $C^0$ integrable Tonelli Hamiltonian are zero and deduce that the metric and topological entropies va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6076","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"}