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

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 $V_{n,r}$.

Funding Agency Grant Number
Ministerio de Economía y Competitividad de España MTM2016-80276-P
PGC2018-098676-B-I00/AEI/FEDER/UE
Catalan Government grant 2017SGR1049
Ministry of Education, Science and Technical Development of Serbia
The research of B. Jovanović was supported by the Serbian Ministry of Education, Science and Technological Development through the Mathematical Institute of the Serbian Academy of Sciences and Arts. The research of Yu. N. Fedorov was partially funded by the Spanish MINECO-FEDER grants MTM2016-80276-P and PGC2018-098676-B-I00/AEI/FEDER/UE and the provincial grant 2017SGR1049.


DOI: https://doi.org/10.4213/tm4107

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

Bibliographic databases:

UDC: 517.925.53+514.853+517.933
Received: December 1, 2019
Revised: December 1, 2019
Accepted: June 18, 2020

Citation: Božidar Jovanović, Yuri N. Fedorov, “Discrete Geodesic Flows on Stiefel Manifolds”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 176–188; Proc. Steklov Inst. Math., 310 (2020), 163–174

Citation in format AMSBIB
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\paper Discrete Geodesic Flows on Stiefel Manifolds
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
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\yr 2020
\vol 310
\pages 176--188
\publ Steklov Math. Inst.
\publaddr Moscow
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