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Sibirskii Matematicheskii Zhurnal, 2023, Volume 64, Number 5, Pages 881–894
DOI: https://doi.org/10.33048/smzh.2023.64.501 (Mi smj7803) 		 
On some properties of semi-Hamiltonian systems arising in the problem of integrable geodesic flows on the two-dimensional torus

S. V. Agapovab, Zh. Sh. Fakhriddinova

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2023.64.501
Abstract: Bialy and Mironov demonstrated in a recent series of works that the search for polynomial first integrals of a geodesic flow on the 2-torus reduces to the search for solutions to a system of quasilinear equations which is semi-Hamiltonian. We study the various properties of this system.
Keywords: integrable geodesic flow, polynomial first integral, weakly nonlinear system, semi-Hamiltonian system, Riemann invariants, generalized godograph method, Euler–Poisson–Darboux equation.
Funding agency Grant number
Russian Science Foundation 19-11-00044-П
Received: 14.04.2023
Revised: 02.05.2023
Accepted: 16.05.2023
Document Type: Article
UDC: 517.938
MSC: 35R30
Language: Russian
Citation: S. V. Agapov, Zh. Sh. Fakhriddinov, “On some properties of semi-Hamiltonian systems arising in the problem of integrable geodesic flows on the two-dimensional torus”, Sibirsk. Mat. Zh., 64:5 (2023), 881–894
Citation in format AMSBIB
\Bibitem{AgaFak23}
\by S.~V.~Agapov, Zh.~Sh.~Fakhriddinov
\paper On some properties of semi-Hamiltonian systems arising in the problem of integrable geodesic flows on the two-dimensional torus
\jour Sibirsk. Mat. Zh.
\yr 2023
\vol 64
\issue 5
\pages 881--894
\mathnet{http://mi.mathnet.ru/smj7803}
\crossref{https://doi.org/10.33048/smzh.2023.64.501}
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