Multiparameter Contact Transformations

Abstract

This is a review of multiparameter families of contact transformations and their relationship with the generalized Hamiltonian system. We derive the integrability conditions for the generalized Hamiltonian system and show that when they are satisfied the solutions to this system determine a family of multiparameter contact transformations of the initial conditions. We prove a necessary and sufficient condition for a multiparameter family of contact transformations to be a group and a characterization of the function which describes the group multiplication rule.