{"paper":{"title":"Explicit estimates on the measure of primary KAM tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Luca Biasco, Luigi Chierchia","submitted_at":"2016-12-06T16:47:54Z","abstract_excerpt":"From KAM Theory it follows that the measure of phase points which do not lie on Diophantine, Lagrangian, \"primary\" tori in a nearly--integrable, real--analytic Hamiltonian system is $O(\\sqrt{\\varepsilon})$, if $\\varepsilon$ is the size of the perturbation. In this paper we discuss how the constant in front of $\\sqrt{\\varepsilon}$ depends on the unperturbed system and in particular on the phase--space domain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01903","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"}