Exact topological classification of Hamiltonian flows on smooth two-dimensional surfaces (Q1303350)

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.