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 chaotic region of a time-perturbed classical pendulum depends on the value of the maximal Lyapunov characteristic number, λ. In this respect we calculate the functions λ(l),w(l), λ( ) andw( ), where l denotes the physical length of the pendulum, the strength of the perturbation andw the width of the stochastic layer around the separatrix. We find that all these functions follow power laws. In particular, both λ(l) and w(l) scale as the Lyapunov exponent and the width of the resonance of the unperturbed system, i.e. as l−1/2 and l3/2, respectively. It follows that the width of the stochastic layer is proportional to λ−3 so that, for sufficiently small values of l, stochastic diffusion is restricted to a thin layer and, therefore, practically does not depend on λ.