{"paper":{"title":"A KAM Theorem for finitely differentiable Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Comlan Edmond Koudjinan","submitted_at":"2019-09-09T18:50:57Z","abstract_excerpt":"Given $l>2\\nu>2d\\geq 4$, we prove the persistence of a Cantor--family of KAM tori of measure $O(\\varepsilon^{1/2-\\nu/l})$ for any non--degenerate nearly integrable Hamiltonian system of class $C^l(\\mathscr D\\times\\mathbb{T}^d)$, where $\\mathscr D\\subset \\mathbb{R}^d$ is a bounded domain, provided that the size $\\varepsilon$ of the perturbation is sufficiently small. This extends a result by D. Salamon in \\cite{salamon2004kolmogorov} according to which we do have the persistence of a single KAM torus in the same framework. Moreover, it is well--known that, for the persistence of a single torus,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.04099","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.04099/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}