On Siegel disks of a class of entire maps

  title={On Siegel disks of a class of entire maps},
  author={Saeed Zakeri},
  journal={Duke Mathematical Journal},
  • S. Zakeri
  • Published 15 April 2010
  • Mathematics
  • Duke Mathematical Journal
Let f : C → C be an entire map of the form f(z) = P(z)exp(Q(z)), where P and Q are polynomials of arbitrary degrees (we allow the case Q = 0). Building upon a method pioneered by M. Shishikura, we show that if f has a Siegel disk of bounded type rotation number centered at the origin, then the boundary of this Siegel disk is a quasicircle containing at least one critical point of f. This unifies and generalizes several previously known results. 

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