On the Julia set of a typical quadratic polynomial with a Siegel disk

Abstract

Let 0 < < 1 be an irrational number with continued fraction expansion = [a 1 , a 2 , a 3 , . . .], and consider the quadratic polynomial P : z e 2i z + z 2 . By performing a trans-quasiconformal surgery on an associated Blaschke product model, we prove that if