{"paper":{"title":"Non-hyperbolic closed characteristics on non-degenerate star-shaped hypersurfaces in ${\\bf R}^{2n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Huagui Duan, Hui Liu, Wei Wang, Yiming Long","submitted_at":"2015-10-29T11:18:35Z","abstract_excerpt":"In this paper, we prove that for every index perfect non-degenerate compact star-shaped hypersurface $\\Sigma\\subset{\\bf R}^{2n}$, there exist at least $n$ non-hyperbolic closed characteristics with even Maslov-type indices on $\\Sigma$ when $n$ is even. When $n$ is odd, there exist at least $n$ closed characteristics with odd Maslov-type indices on $\\Sigma$ and at least $(n-1)$ of them are non-hyperbolic. Here we call a compact star-shaped hypersurface $\\Sigma\\subset {\\bf R}^{2n}$ {\\rm index perfect} if it carries only finitely many geometrically distinct prime closed characteristics, and every"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08648","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":""},"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"}