Differentiability of invariants and Liapunov equations in Hamiltonian systems

In this communication, we investigate the behavior of the derivatives of invariants for Hamiltonian systems, using information derived from an analysis of the Liapunov exponents of the system. We show that under certain conditions on the analyticity properties of the solutions of the equations of motion, it is possible to construct 2n invariants of motion which are guaranteed to beC ^∞ as functions of phase space and time in a suitably defined domainD.