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 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D=1 to the cantorus is governed by an exponent ν̅ =0.98… and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent.