{"paper":{"title":"On the mean indices of closed characteristics on dynamically convex star-shaped hypersurfaces in $\\mathbb{R}^{2n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Wei Wang","submitted_at":"2025-06-05T01:35:57Z","abstract_excerpt":"In this paper, we prove that for every dynamically convex compact star-shaped hypersurface $\\Sigma\\subset\\mathbb{R}^{2n}$, there exist at least $\\lfloor\\frac{n+1}{2}\\rfloor$ geometrically distinct closed characteristics possessing irrational mean indices provided the number of geometrically distinct closed characteristics on $\\Sigma$ is finite, this improves Theorem 1.3 in \\cite{LoZ} of Y. Long and C. Zhu by finding one more closed characteristic possessing irrational mean index when $n$ is odd. Moreover, there exist at least $\\lfloor\\frac{n+1}{2}\\rfloor+1$ geometrically distinct closed charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04546","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/2506.04546/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"}