Abstract:
We study integrable geodesic flows on surfaces of revolution (the torus and the Klein bottle). We obtain a Liouville classification of integrable geodesic flows on the surfaces under consideration with potential in the case of a linear integral. Here, the potential is invariant under an isometric action of the circle on the manifold of revolution. This classification is obtained on the basis of calculating the Fomenko-Zieschang invariants (marked molecules) of the systems.
Bibliography: 18 titles.
Citation:
D. S. Timonina, “Liouville classification of integrable geodesic flows in a potential field on two-dimensional manifolds of revolution: the torus and the Klein bottle”, Sb. Math., 209:11 (2018), 1644–1676
\Bibitem{Tim18}
\by D.~S.~Timonina
\paper Liouville classification of integrable geodesic flows in a~potential field on two-dimensional manifolds of revolution: the torus and the Klein bottle
\jour Sb. Math.
\yr 2018
\vol 209
\issue 11
\pages 1644--1676
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https://www.mathnet.ru/eng/sm9009
https://doi.org/10.1070/SM9009
https://www.mathnet.ru/eng/sm/v209/i11/p103
This publication is cited in the following 3 articles:
A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrable systems”, Russian Math. Surveys, 78:5 (2023), 881–954
E. I. Antonov, I. K. Kozlov, “Liuvilleva klassifikatsiya integriruemykh geodezicheskikh potokov na proektivnoi ploskosti v potentsialnom pole”, Chebyshevskii sb., 21:2 (2020), 10–25
A. T. Fomenko, V. V. Vedyushkina, “Implementation of integrable systems by topological, geodesic billiards with potential and magnetic field”, Russ. J. Math. Phys., 26:3 (2019), 320–333
Citation in format AMSBIB
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