Herman's condition and critical points on the boundary of Siegel disks   of polynomials with two critical values
  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. 
Arnaud Ch\'eritat, Pascale Roesch
math.DS