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Exact topological classification of Hamiltonian flows on smooth two-dimensional surfaces. (English. Russian original) Zbl 0952.37020

J. Math. Sci., New York 94, No. 4, 1457-1476 (1999); translation from Zap. Nauchn. Semin. POMI 235, 22-53 (1996).
The authors present an exact classification scheme for all nondegenerate Hamiltonian systems on smooth closed two-dimensional surfaces. In case of Hamiltonians with one degree of freedom it is shown that two smooth Hamiltonian systems are exactly topologically equivalent only in the condition that their exact molecules coincide. The method to classify exact topological equivalence classes for nondegenerate Hamiltonian systems with one degree of freedom is demonstrated.

MSC:

37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)