{"paper":{"title":"Bumpy metrics on spheres and minimal index growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hans-Bert Rademacher","submitted_at":"2016-08-05T17:00:17Z","abstract_excerpt":"The existence of two geometrically distinct closed geodesics on an $n$-dimensional sphere $S^n$ with a non-reversible and bumpy Finsler metric was shown independently by Duan--Long [7] and the author [27]. We simplify the proof of this statement by the following observation: If for some $N \\in \\mathbb{N}$ all closed geodesics of index $\\le N$ of a non-reversible and bumpy Finsler metric on $S^n$ are geometrically equivalent to the closed geodesic $c$ then there is a covering $c^r$ of minimal index growth, i.e. $${\\rm ind}(c^{rm})=m {\\rm ind}(c^r)-(m-1)(n-1)$$ for all $m \\ge 1$ with ${\\rm ind}\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01937","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"}