ON THE RECURRENCE AND LYAPUNOV TIME SCALES OF THE MOTION NEAR THE CHAOS BORDER

Conditions for the emergence of a statistical relationship between T-r , the chaotic transport (recurrence) time, and T-L, the local Lyapunov time (the inverse of the numerically measured largest Lyapunov charac teristic exponent), are considered for the motion inside the chaotic l ayer around the separatrix of a nonlinear resonance. When numeric valu es of the Lyapunov exponents are measured on a time interval not great er than T-r, the relationship is shown to resemble the quadratic one. This tentatively explains numeric results presented in the literature. (C) 1998 Elsevier Science B.V.