The Fine Structure of Herman Rings
classification
🧮 math.DS
keywords
hermanfineringringssiegelstructureblaschkeboundary
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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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