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arXiv · 1511.01522

The Fine Structure of Herman Rings

Núria Fagella·Christian Henriksen
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Abstract

We study the geometric structure of the boundary of Herman rings in a model family of Blaschke products of degree 3. Shishikura's quasiconformal surgery relates the Herman ring to the Siegel disk of a quadratic polynomial. By studying the regularity properties of the maps involved, we can transfer McMullen's results on the fine local geometry of Siegel disks to the Herman ring setting.

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Núria Fagella, Christian Henriksen. 2015-11-04. The Fine Structure of Herman Rings. https://doi.org/10.1007/s12220-017-9764-9

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