The Use of Lie Series in the Construction of a Perturbation Theory and Some Recent Results in the Theory of the Motion of Hyperion

This paper begins with a brief review of a form of the Lie series transformation, and then reports some new results in the study, using Lie series methods, of the orbit of Saturn's satellite Hyperion. In particular, improved expressions are given for the long-period perturbations of the orbital elements which describe the motion in the orbit plane, and also first results for expressions for the short-period perturbations in the apse longitude, derived from the Lie series generating function. This revised version was published online in July 2006 with corrections to the Cover Date.