N. Buric et al., UNIVERSAL SCALING OF CRITICAL QUASI-PERIODIC ORBITS IN A CLASS OF TWIST MAPS, Journal of physics. A, mathematical and general (Print), 31(39), 1998, pp. 7847-7854
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.