Resonance hopping in comets

The motions of ten short-period comets strongly perturbed by Jupiter are discussed in terms of the ''hop'' phenomenon, in which objects move dramatically from one resonance situation to another. It is shown that the ''fuzzy boundary'' concept is useful in trying to develop a theoretical understanding of the situation, and a sketch of a proof is presented. It is suggested that objects associated with the 3:2 and 2:3 resonances are the ones that can become involved in weak or quasi-weak capture as temporary satellites of Jupiter. Otherwise, resonance effects of quite high order, as well as double-resonance effects, play significant dynamical roles that also warrant a mathematical explanation. (C) 1997 American Astronomical Society.