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 language | English |
|---|---|
| Journal | Journal of Geometric Analysis |
| Volume | 27 |
| Issue number | 3 |
| Pages (from-to) | 2381-2399 |
| ISSN | 1050-6926 |
| DOIs | |
| Publication status | Published - 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