The Fine Structure of Herman Rings
N\'uria Fagella, Christian Henriksen
TL;DR
This paper investigates the detailed geometric structure of Herman rings in a specific family of Blaschke products, using quasiconformal surgery to relate them to Siegel disks and transfer known geometric results.
Contribution
It introduces a method to analyze Herman rings by connecting their geometry to Siegel disks through quasiconformal surgery, providing new insights into their fine structure.
Findings
Established a relationship between Herman rings and Siegel disks via surgery.
Transferred McMullen's results to describe Herman ring geometry.
Analyzed regularity properties of the involved maps.
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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