Geodesic
Liouville classification of integrable geodesic flows in a~potential field on two-dimensional manifolds of revolution: the torus and the Klein bottle
Sbornik. Mathematics, Tome 209 (2018) no. 11, pp. 1644-1676

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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.
Keywords: Hamiltonian system, geodesic flow, marked molecule
Mots-clés : Liouville equivalence, Fomenko-Zieschang invariant. 
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     author = {D. S. Timonina},
     title = {Liouville classification of integrable geodesic flows in a~potential field on two-dimensional manifolds of revolution: the torus and the {Klein} bottle},
     journal = {Sbornik. Mathematics},
     pages = {1644--1676},
     publisher = {mathdoc},
     volume = {209},
     number = {11},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2018_209_11_a4/}
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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. Sbornik. Mathematics, Tome 209 (2018) no. 11, pp. 1644-1676. http://geodesic.mathdoc.fr/item/SM_2018_209_11_a4/