Siegel disc singularity spectra

The author numerically determines the generalized dimensions and spectrum of singularities of a critical point orbit on the boundary of a Siegel disc. The local scaling exponent, alpha _MN, and spectrum dependence on the degree, d, of the critical point are also considered. He finds that lim _{d to infinity} mod alpha _MN mod ^d approximately=0.523 53 and hence, asymptotically, the lower limit of the spectrum is constant whilst the upper limit is proportional to d.