Classification of bifurcations emerging in the case of non-compact isoenergetic surfaces

Galina Goujvina (WhiteDogy@rambler.ru )
Moscow State University
B. Dmitrovka Str.,
14-9 107 031 Moscow, Russia

Abstract

We consider a hamiltonian system with two degrees of freedom on a 4-dimentional simplectical manifold integrable with the help of two integrals H and f. According to the famous Liouville theorem the non-singular common level surfaces of these integrals can be represented as the union of tori, cylinders and planes. The case of compact surfaces and there bifurcations on the singularities has already been investigated by prof. Fomenko; my work contains the investigation of the problem in non-compact case.