Geodesic
A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom
Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 567-596

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A new topological invariant is constructed which classifies integrable Hamiltonian systems with two degrees of freedom (admitting a Bott integral). A criterion for the equivalence of Bott systems is proved: such systems are topologically equivalent if and only if their topological invariants coincide. The topological invariant is effectively calculated for specific integrable Hamiltonian systems in physics and mechanics. 
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     author = {A. T. Fomenko and H. Zieschang},
     title = {A topological invariant and a criterion for the equivalence of integrable {Hamiltonian} systems with two degrees of freedom},
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A. T. Fomenko; H. Zieschang. A topological invariant and a criterion for the equivalence of integrable Hamiltonian systems with two degrees of freedom. Izvestiya. Mathematics , Tome 36 (1991) no. 3, pp. 567-596. http://geodesic.mathdoc.fr/item/IM2_1991_36_3_a5/