Tulczyjew's triplet for Lie groups III : higher order dynamics and reductions for iterated bundles

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.