EQUIVALENT CLASSES OF CRITICAL CIRCLES

We present numerical evidence that the fractal properties of the criti cal invariant circles of a typical area-preserving twist map, as summa rized by the f(alpha) spectrum and the generalized dimensions D(q), de pend only on the tails in the continued fraction expansion of the corr esponding rotation numbers. f(alpha) and D(q) are numerically the same for all critical invariant circles of the standard and sine maps whic h have the rotation numbers with the same periodic tail.