Perturbations in a champagne bottle - Georgiev, Georgy (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1997)
The system describing the motion of a particle in a potential field shaped like the bottom of a champagne bottle (more precisely, an $S^{1}$ symmetric double well) for KAM-theory conditions is studied. We show that the Kolmogorov's condition is fulfilled everywhere out of the bifurcation diagram of the energy-momentum map and we make researches for the condition of isoenergetical non-degeneracy.