This article is cited in 5 papers

Liouville classification of integrable geodesic flows in a potential field on two-dimensional manifolds of revolution: the torus and the Klein bottle

D. S. Timonina

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University

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.

Keywords: Hamiltonian system, Liouville equivalence, geodesic flow, marked molecule, Fomenko-Zieschang invariant.

UDC: 514.853

MSC: Primary 37J35; Secondary 37G10, 37J20

Received: 08.09.2017 and 12.12.2017

DOI: 10.4213/sm9009

 English version: Sbornik: Mathematics, 2018, 209:11, 1644–1676

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