Quasi-symmetric conjugacy of Blaschke products on the unit circle

Let B be a Blaschke product for which the restriction to theunit circle ¹ is a degree d > 1 covering. We prove that Bis quasi-symmetrically conjugate to z z^d on ¹, if all its periodicpoints in ¹ are repelling and if ¹ does not intersect the -limitset of any recurrent critical point for B.