{"paper":{"title":"Lagrangian tori near resonances of near-integrable Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anatoly Neishtadt, Anton Medvedev, Dmitry Treschev","submitted_at":"2013-11-01T10:09:09Z","abstract_excerpt":"In this paper we study families of Lagrangian tori that appear in a neighborhood of a resonance of a near-integrable Hamiltonian system. Such families disappear in the \"integrable\" limit $\\varepsilon\\to 0$. Dynamics on these tori is oscillatory in the direction of the resonance phases and rotating with respect to the other (non-resonant) phases.\n  We also show that, if multiplicity of the resonance equals one, generically these tori occupy a set of large relative measure in the resonant domains in the sense that the relative measure of the remaining \"chaotic\" set is of order $\\sqrt\\varepsilon$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0132","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"}