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Critical points on the boundaries of Siegel disks


Author: James T. Rogers
Journal: Bull. Amer. Math. Soc. 32 (1995), 317-321
MSC: Primary 30D05; Secondary 54F15, 58F23
DOI: https://doi.org/10.1090/S0273-0979-1995-00600-2
MathSciNet review: 1316499
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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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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1995-00600-2
Keywords: Siegel disk, critical point, Julia set, Fatou set, indecomposable continuum, prime end
Article copyright: © Copyright 1995 American Mathematical Society

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