Geodesic
Liouville classification of integrable geodesic flows on a torus of revolution in a potential field
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2017), pp. 35-43

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A Liouville classification of integrable Hamiltonian systems being geodesic flows on a 2-dimensional torus of revolution in an invariant potential field in the case of linear integral is obtained. This classification is obtained using the Fomenko–Zieschang invariant (marked molecules) of studied systems. All types of bifurcation curves are described. A classification of singularities of the system solutions is also obtained. 
@article{VMUMM_2017_3_a4,
     author = {D. S. Timonina},
     title = {Liouville classification of integrable geodesic flows on a torus of revolution in a potential field},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {35--43},
     publisher = {mathdoc},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_3_a4/}
}
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D. S. Timonina. Liouville classification of integrable geodesic flows on a torus of revolution in a potential field. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2017), pp. 35-43. http://geodesic.mathdoc.fr/item/VMUMM_2017_3_a4/