Stochastic dynamics of nuclei quadrupole oscillations and normal forms of Birghoff-Gustavson

It is proposed for correct determination of critical energy for transition from regular motion to chaotic one in potential with several local minima by negative curvature criterium to supplement the latter one by analysis in each minimum of the fixed point number, which in their turn are determined by motion additional integral structure. The motion additional integrals are derived by reducing corresponding hamiltonian to Birghoff-Gustavson normal forms. The study is carried out using the potential of nuclei quadrupole surface oscillations