{"paper":{"title":"On the dynamics of contact Hamiltonian systems II: Variational construction of asymptotic orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jun Yan, Kai Zhao, Liang Jin","submitted_at":"2025-01-02T14:31:27Z","abstract_excerpt":"This paper is a continuation of our study of the dynamics of contact Hamiltonian systems in \\cite{JY}, but without monotonicity assumption. Due to the complexity of general cases, we focus on the behavior of action minimizing orbits. We pick out certain action minimizing invariant sets $\\{\\widetilde{\\mathcal{N}}_u\\}$ in the phase space naturally stratified by solutions $u$ to the corresponding Hamilton-Jacobi equation. Using an extension of characteristic method, we establish the existence of semi-infinite orbits that is asymptotic to some $\\widetilde{\\mathcal{N}}_u$ and heteroclinic orbits be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01279","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.01279/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"}