{"paper":{"title":"Melnikov's persistence for completely degenerate Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jiayin Du, Shuguan Ji, Yong Li","submitted_at":"2022-12-31T14:02:27Z","abstract_excerpt":"In this paper, we study the Melnikov's persistence for completely degenerate Hamiltonian systems with the following Hamiltonian \\begin{equation*} H(x,y,u,v)=h(y)+g(u,v)+\\varepsilon P(x,y,u,v),~~~(x,y,u,v)\\in \\mathbb{T}^n\\times{G}\\times \\mathbb{R}^d\\times \\mathbb{R}^d, \\end{equation*} where $n\\geq2$ and $d\\geq1$ are positive integers, $G\\subset\\mathbb{R}^n$, $g=o(|u|^2+|v|^2)$ admits complete degeneracy and certain transversality, and $\\varepsilon P$ is the small perturbation. This is a try in studying lower-dimensional invariant tori in the normal complete degeneracy. Under R\\\"{u}ssmann-like n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.00206","kind":"arxiv","version":3},"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/2301.00206/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"}