{"paper":{"title":"Orbits of nearly integrable systems accumulating to KAM tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Marcel Guardia, Vadim Kaloshin","submitted_at":"2014-12-22T18:36:08Z","abstract_excerpt":"Consider a sufficiently smooth nearly integrable Hamiltonian system of two and a half degrees of freedom in action-angle coordinates \\[\n  H_\\epsilon (\\varphi,I,t)=H_0(I)+\\epsilon H_1(\\varphi,I,t), \\varphi\\in T^2,\\ I\\in U\\subset R^2,\\ t\\in T=R/Z. \\] Kolmogorov-Arnold-Moser Theorem asserts that a set of nearly full measure in phase space consists of three dimensional invariant tori carrying quasiperiodic dynamics.\n  In this paper we prove that for a class of nearly integrable Hamiltonian systems there is an orbit which contains these KAM tori in its $\\omega$-limit set. This implies that the clos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7088","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"}