TULCZYJEW'S TRIPLET FOR LIE GROUPS III: HIGHER ORDER DYNAMICS AND REDUCTIONS FOR ITERATED BUNDLES

Abstract

Given a Lie group G , we elaborate the dynamics on T * T * G and T * T G , which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space TT * G , which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.