{"paper":{"title":"Variational attraction of the KAM torus for the conformally symplectic system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DS","authors_text":"Jianlu Zhang, Kai Zhao, Liang Jin","submitted_at":"2020-09-26T08:13:50Z","abstract_excerpt":"For the conformally symplectic system \\[ \\left\\{ \\begin{aligned} \\dot{q}&=H_p(q,p),\\quad(q,p)\\in T^*\\mathbb{T}^n\\\\ \\dot p&=-H_q(q,p)-\\lambda p, \\quad \\lambda>0 \\end{aligned} \\right. \\] with a positive definite Hamiltonian, we discuss the variational significance of invariant Lagrangian graphs and explain how the KAM torus impacts the $W^{1,\\infty}-$convergence speed of the Lax-Oleinik semigroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.12532","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/2009.12532/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"}