Geodesic
The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability
Izvestiya. Mathematics , Tome 29 (1987) no. 3, pp. 629-658

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The surfaces of constant energy in integrable Hamiltonian systems which possess Bott integrals are classified. A complete topological classification is given of surgery of Liouville tori in general position in integrable Hamiltonian systems. Bibliography: 28 titles. 
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     author = {A. T. Fomenko},
     title = {The topology of surfaces of constant energy in integrable {Hamiltonian} systems, and obstructions to integrability},
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A. T. Fomenko. The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability. Izvestiya. Mathematics , Tome 29 (1987) no. 3, pp. 629-658. http://geodesic.mathdoc.fr/item/IM2_1987_29_3_a6/