Lyapunov Numbers and Stochastic Layer Widths in a Perturbed Pendulum
Abstract
We examine whether the macroscopically measured diffusion rate in the chaotic region of a perturbed classical pendulum depends on the value of the Lyapunov Characteristic Number, lambda. In this respect we calculate 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 perturbation and w the width of the stochastic layer around the separatrix. We find that all these functions follow power laws. In particular both lambda (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 l^{3/2} respectively. It follows that the width of the stochastic layer is inversely proportional to the cube of lambda so that, for sufficiently small values of l, diffusion is restricted to a thin layer and therefore practically does not depend on lambda.
 Publication:

Joint European and National Astronomical Meeting
 Pub Date:
 1997
 Bibcode:
 1997jena.confE..26T