{"paper":{"title":"Resonance identity and multiplicity of non-contractible closed geodesics on Finsler $\\mathbb{R}P^{n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.DS","authors_text":"Hui Liu, Yuming Xiao","submitted_at":"2016-07-10T13:44:36Z","abstract_excerpt":"In this paper, we establish first the resonance identity for non-contractible homologically visible prime closed geodesics on Finsler $n$-dimensional real projective space $(\\mathbb{R}P^n,F)$ when there exist only finitely many distinct non-contractible closed geodesics on $(\\mathbb{R}P^n,F)$, where the integer $n\\geq2$. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics on $\\mathbb{R}P^{n}$ with a bumpy and irreversible Finsler metric. Together with two previous results on bumpy and reversible Finsler metrics in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02746","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"}