Universal small-scale structure near the boundary of siegel disks of arbitrary rotation number

Abstract 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 renormalisation operator.

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