Abstract
Abstract Energy surfaces in the space of action variables are calculated and graphically presented for general triaxial ellipsoidal billiards. As was demonstrated by Jacobi in 1838, the system may be integrated in terms of hyperelliptic functions. The actual computation, however, has never been done. It is found that generic energy surfaces consist of seven pieces, representing topologically different types of invariant tori. The character of the corresponding motion is discussed. Frequencies, winding numbers, and the location of resonances are also determined. The results may serve as a basis for perturbation theory of slightly modified systems, and for semi-classical quantization.
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