ON THE EXISTENCE OF HIGHER-ORDER LYAPUNOV EXPONENTS

We prove the existence of an exponential rate of growth for the second derivative of a one-dimensional dynamical system with positive Lyapun ov exponent, and prove that the second order Lyapunov exponent thus de fined is equal to precisely twice the first order derivative. Similar techniques shed some light on the multidimensional case. This work ext ends results of Dressler and Farmer, and verifies a conjecture of Farm er and Sidorowich related to a priori estimates for time series foreca sting.