Lie Series Perturbation Theory

Abstract

In 1966, the Poincaré and von Zeipel-Brouwer theories were rejuvenated by Hori [53] through the introduction of canonical transformations expressed by Lie series mappings instead of the classical Jacobian transformations. The use of mathematical operations in perturbation theories with the same properties as Lie derivatives and Lie series was already current among physicists [13] and, around 1960, in at least one instance (Sérsic [85]), it was suggested that Lie series could be used to represent the canonical transformations of Celestial Mechanics.