Some remarks on high degree polynomial integrals of the magnetic geodesic flow on the two-dimensional torus

DOI10.1134/S0037446621040017zbMath1483.37071OpenAlexW3198188101WikidataQ114075219 ScholiaQ114075219MaRDI QIDQ820453

V. V. Shubin, Alexandr Valyuzhenich, Sergey Agapov

Publication date: 27 September 2021

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446621040017

zbMATH Keywords

magnetic geodesic flowpolynomial first integral

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geodesic flows in symplectic geometry and contact geometry (53D25) Flows on surfaces (37E35) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (1)

Integrable magnetic geodesic flows on 2-surfaces ^*

Cites Work

• On first integrals of geodesic flows on a two-torus
• Integrable magnetic geodesic flows on 2-torus: new examples via quasi-linear system of PDEs
• On first integrals of two-dimensional geodesic flows
• Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels
• GEODESIC FLOWS ON TWO-DIMENSIONAL MANIFOLDS WITH AN ADDITIONAL FIRST INTEGRAL THAT IS POLYNOMIAL IN THE VELOCITIES
• Integrable Hamiltonian systems with velocity-dependent potentials

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