{"paper":{"title":"KAM-tori near an analytic elliptic fixed point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"B. Fayad, H. Eliasson, R. Krikorian","submitted_at":"2014-01-22T18:25:54Z","abstract_excerpt":"We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector $\\o_0$ is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\\\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that $\\o_0$ has rationally independent coo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5748","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"}