02-7   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Lasse Rempe:

An Answer to a Question of Herman, Baker and Rippon Concerning Siegel Disks

We show that, for the family of exponential maps $z\mapsto \exp(z)+\kappa$, a Siegel disk $U$ is unbounded if and only if its boundary contains the singular value $\kappa$. In particular, this implies by a result of Herman that $\kappa\in \partial U$ if the rotation number is diophantine.

Mathematics Subject Classification (1991): Primary: 37F10; Secondary 30D05

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[Thu Feb 19 18:56:36 2009]
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