The computation of Lyapunov exponents for periodic trajectories

We present a new method for the numerical computation of Lyapunov exponents of periodic trajectories which is crucial in the investigation of dynamics. The computational time of this method is merely a period of the periodic trajectory considered, when Lyapunov exponents call be approximated as precise as one wants. Our method stems from a combination between Floquet theory on periodic linear differential systems and Lie group methods in structure preserving algorithms on manifolds. The Lyapunov exponents of a periodic trajectory of the Lorenz system and a periodic solitary wave of the nonlinear Schrodinger equation with periodic coefficients are investigated by using the method.