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On a symplectical manifold M 4 consider a Hamiltonian system with two degrees of freedom, integrable with the help of an additional integral f. According to the well-known Liouville theorem, non-singular level surfaces of the integrals H and f can be represented as unions of tori, cylinders and planes. The classification of bifurcations of the compact level surfaces was given by Professor A. Fomenko and his school. This paper generalizes this result to the non-compact surfaces.

journal of nonlinear mathematical physics

The Classification of the Bifurcations Emerging in the case of an Integrable Hamiltonian System with Two Degrees of Freedom when an Isoenergetic Surface is Non-Compact