{"paper":{"title":"Integrable flows and Backlund transformations on extended Stiefel varieties with application to the Euler top on the Lie group SO(3)","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Yuri N. Fedorov","submitted_at":"2005-05-18T02:13:06Z","abstract_excerpt":"We show that the $m$-dimensional Euler--Manakov top on $so^*(m)$ can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety $\\bar{\\cal V}(k,m)$, and present its Lax representation with a rational parameter.\n  We also describe an integrable two-valued symplectic map $\\cal B$ on the 4-dimensional variety ${\\cal V}(2,3)$. The map admits two different reductions, namely, to the Lie group SO(3) and to the coalgebra $so^*(3)$.\n  The first reduction provides a discretization of the motion of the classical Euler top in space and has a transpa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0505045","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"}