Universal small-scale structure near the boundary of Siegel disks of arbitrary rotation number (Q1088236)

We present numerical evidence that for analytic maps of the complex plane with a Siegel disk of any irrational rotation number and a quadratic critical point on its boundary, the small scale structure near the critical point can be described asymptotically by a universal two- parameter family. We propose an explanation in terms of an ergodic attractor for a renormalization operator.