with Df being a matrix with elements [Df ] jk = ∂f j /∂z k . The Hamilton's equations of motion along with the variational equation above are integrated for a given initial phase space point z 0 and a fixed initial vector v 0 . Note that the time evolution of the tangent vector for regular and chaotic trajectories is distinctly different, and in the inset to Fig. we show an example for our model system.