Critical points on the boundaries of Siegel disks

Rogers, James T.

doi:10.1090/S0273-0979-1995-00600-2

Critical points on the boundaries of Siegel disks
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Bull. Amer. Math. Soc. 32 (1995), 317-321 Request permission

Abstract:

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.

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