On the relation between the maximal LCN and the width of the stochastic layer in a driven pendulum

We examine whether the macroscopically measured diffusion rate in the chaot ic region of a time-perturbed classical pendulum depends on the value of th e maximal Lyapunov characteristic number, lambda. In this respect we calcul ate the functions lambda(l), w(l), lambda(epsilon) and w(epsilon), where l denotes the physical length of the pendulum, epsilon the strength of the pe rturbation and w the width of the stochastic layer around the separatrix. W e find that all these functions follow power laws. In particular, both lamb da(l) and w(l) scale as the Lyapunov exponent and the width of the resonanc e of the unperturbed system, i.e, as l(-1/2) and l(3/2), respectively. It f ollows that the width of the stochastic layer is proportional to lambda(-3) so that, for sufficiently small values of l, stochastic diffusion is restr icted to a thin layer and, therefore, practically does not depend on lambda .