The Fine Structure of Herman Rings

Nuria 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 (up to quasiconformal deformation). 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 transfer McMullen’s results on the fine local geometry of Siegel disks to the Herman ring setting.
Original languageEnglish
JournalJournal of Geometric Analysis
Volume27
Issue number3
Pages (from-to)2381-2399
ISSN1050-6926
DOIs
Publication statusPublished - 2017

Keywords

  • Mathematics
  • Differential Geometry
  • Convex and Discrete Geometry
  • Fourier Analysis
  • Abstract Harmonic Analysis
  • Dynamical Systems and Ergodic Theory
  • Global Analysis and Analysis on Manifolds
  • SC10
  • Holomorpphic dynamics
  • Herman rings
  • Julia set
  • Self-similarity

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