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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 295, Pages 241–260
DOI: https://doi.org/10.1134/S0371968516040154 (Mi tm3760) 		 
This article is cited in 18 scientific papers (total in 18 papers)

On first integrals of geodesic flows on a two-torus

I. A. Taimanovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090 Russia
b Faculty of Mechanics and Mathematics, Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
Full-text PDF (245 kB) Citations (18)
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DOI: https://doi.org/10.1134/S0371968516040154
Abstract: For a geodesic (or magnetic geodesic) flow, the problem of the existence of an additional (independent of the energy) first integral that is polynomial in momenta is studied. The relation of this problem to the existence of nontrivial solutions of stationary dispersionless limits of two-dimensional soliton equations is demonstrated. The nonexistence of an additional quadratic first integral is established for certain classes of magnetic geodesic flows.
Funding agency Grant number
Russian Science Foundation 14-11-00441
This work is supported by the Russian Science Foundation under grant 14-11-00441.
Received: May 26, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 295, Pages 225–242
DOI: https://doi.org/10.1134/S0081543816080150
Bibliographic databases:
Document Type: Article
UDC: 517.9+531.01
Language: Russian
Citation: I. A. Taimanov, “On first integrals of geodesic flows on a two-torus”, Modern problems of mechanics, Collected papers, Trudy Mat. Inst. Steklova, 295, MAIK Nauka/Interperiodica, Moscow, 2016, 241–260; Proc. Steklov Inst. Math., 295 (2016), 225–242
Citation in format AMSBIB
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    • This publication is cited in the following 18 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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