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.
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Acknowledgment
The authors thank an anonymous referee for useful remarks.
Funding
Agapov was supported by the Russian Science Foundation (Grant no. 19–11–00044–P).
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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 5, pp. 881–894. https://doi.org/10.33048/smzh.2023.64.501
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Agapov, S.V., Fakhriddinov, Z.S. On Some Properties of Semi-Hamiltonian Systems Arising in the Problem of Integrable Geodesic Flows on the Two-Dimensional Torus. Sib Math J 64, 1063–1075 (2023). https://doi.org/10.1134/S0037446623050014
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DOI: https://doi.org/10.1134/S0037446623050014
Keywords
- integrable geodesic flow
- polynomial first integral
- weakly nonlinear system
- semi-Hamiltonian system
- Riemann invariants
- generalized godograph method
- Euler–Poisson–Darboux equation