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. 
@article{MZM_1997_61_2_a1,
     author = {B. S. Kruglikov},
     title = {Exact smooth classification of hamiltonian vector fields on two-dimensional manifolds},
     journal = {Matemati\v{c}eskie zametki},
     pages = {179--200},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a1/}
}
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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/