Perturbations in a champagne bottle - Georgiev, Georgy (Ann. Sofia Univ. Fac. Math. and Inf., 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.