Conservation of the Tisserand parameter at close encounters of interplanetary objects with Jupiter

This article has a long story. It was first written between 1979 and 1981, at the beginning of our cooperation with ubor Kresák. The goal of the paper was to check the conservation of various formulations of the Tisserand parameter and to investigate the relationships between theT-values and the dynamical behaviours at close encounters with Jupiter. A first draft of the paper was subsequently enlarged and revised in 1983, as new findings led us to the addition of another substantial section. Then, the paper has remained in a draft version up to now, being modified from time to time because of our committments with the computations of long-term evolutions of short-period comets. We want to honour the memory of ubor letting this article finally come out.Andrea Carusi and Giovanni B. Valsecchi, Rome, 1994