ELLIPSOIDAL BILLIARDS WITH ISOTROPIC HARMONIC POTENTIALS

Abstract

The classical dynamics of the triaxial ellipsoidal billiard with isotropic harmonic potential attracting to the center of the ellipsoid is discussed. The integrability preserving potential introduces an energy dependence to the foliation of energy shells into invariant tori. This foliation and the character of the corresponding motion is described in terms of 13 qualitatively different energy surfaces in the space of the action variables. Frequencies and the location of resonances are calculated. The consequences of the superintegrability of the low-energy case, the isotropic harmonic oscillator, for the energy surfaces in action space are investigated.