Geodesic
Exact smooth classification of hamiltonian vector fields on two-dimensional manifolds
Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 179-200.

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A complete exact classification of Hamiltonian systems with Morse Hamiltonians on two-dimensional manifolds is given, i.e., the systems are classified up to diffeomorphisms mapping vector fields into vector fields. The classification imposes no restrictions on Morse functions. 
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B. S. Kruglikov. Exact smooth classification of hamiltonian vector fields on two-dimensional manifolds. Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 179-200. http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a1/

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