Herman's condition and critical points on the boundary of Siegel disks of polynomials with two critical values (1111.4629v3)

Abstract: We extend a theorem of Herman from the case of unicritical polynomials to the case of polynomials with two finite critical values. This theorem states that Siegel disks of such polynomials, under a diophantine condition (called Herman's condition) on the rotation number, must have a critical point on their boundaries.