Critical points on the boundaries of Siegel disks

Bull. Amer. Math. Soc. (N.S.) 32 (1995) 317-321 Let $f$ be a polynomial map of the Riemann sphere of degree at least two. We prove that if $f$ has a Siegel disk $G$ on which the rotation number satisfies a diophantine condition, then the boundary of $G$ contains a critical point.