Lyapunov spectra of hamiltonian systems using reduced tangent dynamics

Recently a reduced formulation of tangent dynamics for computing the Lyapunov spectrum of a Hamiltonian system has been developed, using its symplectic structure [Partovi, Phys. Rev. Lett. 82, 3424 (1999)]. In this paper, we make a detailed numerical comparison of this formulation with a standard algorithm, by applying both to some typical Hamiltonian systems with two and three degrees of freedom. For the latter, we cast the reduced dynamics in a form convenient for computations, and capable of generalization to a higher number of degrees of freedom. The numerical values of the positive Lyapunov exponents coincide in most cases and the convergence rates are also comparable. However, the CPU time required for computation is invariably higher for the reduced formulation, making it less efficient than the standard algorithm.