Local Lyapunov exponents in chaotic systems

Abstract We define a local Lyapunov exponent in chaotic systems so that the Lyapunov exponent along a trajectory is the integral over the local exponent, thus extending previously used short time Lyapunov exponents to a pointwise definition. Calculations are presented for the dissipative Lorenz system, the conservative Chirikov-Taylor standard map, and a 3D volume preserving flow of interest in magnetohydrodynamics.