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arXiv · 1211.4535

Singular values and bounded Siegel disks

Anna Miriam Benini·Nuria Fagella
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Abstract

Let $f$ be an entire transcendental function of finite order and $Δ$ be a forward invariant bounded Siegel disk for $f$ with rotation number in Herman's class $\mathcal{H}$. We show that if $f$ has two singular values with bounded orbit, then the boundary of $Δ$ contains a critical point. We also give a criterion under which the critical point in question is recurrent. We actually prove a more general theorem with less restrictive hypotheses, from which these results follow.

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Anna Miriam Benini, Nuria Fagella. 2014-07-29. Singular values and bounded Siegel disks. https://arxiv.org/abs/1211.4535

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