{"paper":{"title":"Geodesic equivalence and integrability","license":"","headline":"","cross_cats":["math.SG","nlin.SI","solv-int"],"primary_cat":"math.DG","authors_text":"Petar J. Topalov, Vladimir S. Matveev","submitted_at":"1999-11-10T10:06:35Z","abstract_excerpt":"We suggest a construction that, given a trajectorial diffeomorphism between two Hamiltonian systems, produces integrals of them.\n As the main example we treat geodesic equivalence of metrics.\n We show that the existence of a non-trivially geodesically equivalent metric leads to Liouville integrability, and present explicit formulae for integrals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911062","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":""},"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"}