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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2020 Volume 310, Pages 176–188 (Mi tm4107)

This article is cited in 1 paper

Discrete Geodesic Flows on Stiefel Manifolds

Božidar Jovanovića, Yuri N. Fedorovb

a Mathematical Institute SANU, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000 Belgrade, Serbia
b Department of Mathematics, Polytechnic University of Catalonia, C. Pau Gargallo 14, 08028 Barcelona, Spain

Abstract: We study integrable discretizations of geodesic flows of Euclidean metrics on the cotangent bundles of the Stiefel manifolds $V_{n,r}$. In particular, for $n=3$ and $r=2$, after the identification $V_{3,2}\cong \mathrm {SO}(3)$, we obtain a discrete analog of the Euler case of the rigid body motion corresponding to the inertia operator $I=(1,1,2)$. In addition, billiard-type mappings are considered; one of them turns out to be the “square root” of the discrete Neumann system on $V_{n,r}$.

Keywords: discrete geodesic flows, noncommutative integrability, canonical transformations, quadratic matrix equations, billiards.

UDC: 517.925.53+514.853+517.933

Received: December 1, 2019
Revised: December 1, 2019
Accepted: June 18, 2020

DOI: 10.4213/tm4107


 English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 310, 163–174

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© Steklov Math. Inst. of RAS, 2025