Lyapunov Exponents. Ii

almost always. For example, λ = ln(2) is experimentally verified for the logistic case f(x) = 4x (1 − x) and u0 = 1/3. This definition is meaningful as well for multidimensional maps f : R → R. It is not true, however, that the norm of a product of Jacobian matrices is equal to the product of their norms; thus the calculational technique (based on the chain rule) used in [2] fails for m > 1. Consider the classical Lorenz system [3, 4, 5, 6, 7]  dx/dt = −10(x− y), x(0) = 0, dy/dt = 28x− y − x z, y(0) = 1, dz/dt = x y − 8 3 z, z(0) = 0