Abstract
We investigate the distortion of Assouad dimension and the Assouad spectrum under Euclidean quasiconformal maps. Our results complement existing conclusions for Hausdorff and box-counting dimension due to Gehring–Väisälä and others. As an application, we classify polynomial spirals (Formula presented.) up to quasiconformal equivalence, up to the level of the dilatation. Specifically, for (Formula presented.) we show that there exists a quasiconformal map (Formula presented.) of (Formula presented.) with dilatation (Formula presented.) and (Formula presented.) if and only if (Formula presented.).
Original language | English (US) |
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Pages (from-to) | 282-307 |
Number of pages | 26 |
Journal | Bulletin of the London Mathematical Society |
Volume | 55 |
Issue number | 1 |
Early online date | Sep 13 2022 |
DOIs | |
State | Published - Feb 2023 |
ASJC Scopus subject areas
- General Mathematics