{"paper":{"title":"On the measure of Lagrangian invariant tori in nearly--integrable mechanical systems (draft)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"L. Biasco, L. Chierchia","submitted_at":"2015-03-27T16:53:55Z","abstract_excerpt":"Consider a real--analytic nearly--integrable mechanical system with potential $f$, namely, a Hamiltonian system, having a real-analytic Hamiltonian $$ H(y,x)=\\frac12 | y |^2 +\\e f(x)\\ , $$\n  $y,x$ being $n$--dimensional standard action--angle variables (and $|\\cdot|$ the Euclidean norm). Then, for \"general\" potentials $f$'s and $\\e$ small enough, the Liouville measure of the complementary of invariant tori is smaller than $\\e|\\ln \\e|^a$ (for a suitable $a>0$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08145","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"}