Fractal Dimension of Cantori

At a critical point the golden-mean Kolmogrov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is $D=0\mathrm{}$ and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension $D=1\mathrm{}$ to the cantorus is governed by an exponent $\overline{\nu }=0.98\mathrm{}\dots$ and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent.