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arXiv · 1906.06802

Siegel disks of the tangent family

Weiwei Cui·Hongming Nie
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Abstract

We study Siegel disks in the dynamics of functions from the tangent family. In particular, we prove that a forward invariant Siegel disk is unbounded if and only if it contains at least one asymptotic value on the boundary. Our argument is elementary and function-theoretic. Moreover, by using quasiconformal surgery we also construct functions in the above family with bounded Siegel disks.

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Weiwei Cui, Hongming Nie. 2019-06-17. Siegel disks of the tangent family. https://arxiv.org/abs/1906.06802

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