On the concept of stationary Lyapunov basis

We propose the concept of stationary Lyapunov basis - the basis of tangent vectors e((i))(x) defined at every point x of the attractor of the dynamical system, and show that one can reformulate some algorithms for calculation of Lyapunov exponents lambda(i) so that each lambda(i) can be treated as the average of a function S-i (x). This enables one to use measure averaging in theoretical arguments thus proposing the rigorous basis for a number of ideas for calculation of Lyapunov exponents from time series. We also study how the Lyapunov vectors in Benettin's algorithm converge to the stationary basis and show that this convergence rate determines continuity of the field of stationary Lyapunov vectors. (C) 1998 Elsevier Science B.V.