RESONANCE HOPPING IN COMETS

The motions of ten short-period comets strongly perturbed by Jupiter a re discussed in terms of the ''hop'' phenomenon, in which objects move dramatically from one resonance situation to another. It is shown tha t the ''fuzzy boundary'' concept is useful in trying to develop a theo retical understanding of the situation, and a sketch of a proof is pre sented. It is suggested that objects associated with the 3:2 and 2:3 r esonances are the ones that can become involved in weak or quasi-weak capture as temporary satellites of Jupiter. Otherwise, resonance effec ts of quite high order, as well as double-resonance effects, play sign ificant dynamical roles that also warrant a mathematical explanation. (C) 1997 American Astronomical Society.