Exact smooth classification of Hamiltonian vector fields on two-dimensional manifolds (Q1274037)

The paper presents a complete trajectory classification of integrable Hamiltonian systems in general position with two degrees of freedom on isoenergetic surfaces in the category \(C^0\). The problem under consideration in many cases can be reduced to the exact classification (in the category \(C^0\)) of Hamiltonian systems in general position with one degree of freedom near a critical leaf of the foliation of the surface of the trajectories. A similar reduction is also feasible in the category of \(C^k\)-smooth maps. The classification imposes no restrictions on Morse functions.