{"paper":{"title":"Algebraic Closed Geodesics on a Triaxial Ellipsoid","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Yuri Fedorov","submitted_at":"2005-06-29T20:05:34Z","abstract_excerpt":"We propose a simple method of explicit description of families of closed geodesics on a triaxial ellipsoid $Q$ that are cut out by algebraic surfaces in ${\\mathbb R}^3$. Such geodesics are either connected components of spatial elliptic curves or rational curves.\n  Our approach is based on elements of the Weierstrass--Poncar\\'e reduction theory for hyperelliptic tangential covers of elliptic curves and the addition law for elliptic functions.\n  For the case of 3-fold and 4-fold coverings, explicit formulas for the cutting algebraic surfaces are provided and some properties of the corresponding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0506063","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"}