Is the boundary of a Siegel disk a Jordan curve?

Rogers, James T.

doi:10.1090/S0273-0979-1992-00324-5

Is the boundary of a Siegel disk a Jordan curve?
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Bull. Amer. Math. Soc. 27 (1992), 284-287 Request permission

Abstract:

Bounded irreducible local Siegel disks include classical Siegel disks of polynomials, bounded irreducible Siegel disks of rational and entire functions, and the examples of Herman and Moeckel. We show that there are only two possibilities for the structure of the boundary of such a disk: either the boundary admits a nice decomposition onto a circle, or it is an indecomposable continuum.

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Indecomposable continua, prime ends and Julia sets

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