UNIVERSAL SCALING OF CRITICAL QUASI-PERIODIC ORBITS IN A CLASS OF TWIST MAPS

Recently we have shown that the fractal properties of the critical inv ariant circles of the standard map, as summarized by the f(alpha) spec trum and the generalized dimensions D(q), depend only on the tails in the continued fraction expansion of the corresponding rotation numbers in (Buric N, Mudrinic M and Todorovic K 1997 J. Phys. A: Math. Gen. 3 0 L161). In the present paper this result is extended on the whole cla ss of sufficiently smooth area-preserving twist maps of cylinders. We present numerical evidence that the f(alpha) and D(q) are the same for all critical invariant circles of any such map which have the rotatio n numbers with the same tail.