Quasiconformal distortion of the Assouad spectrum and classification of polynomial spirals

Efstathios K. Chrontsios Garitsis, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)282-307
Number of pages26
JournalBulletin of the London Mathematical Society
Volume55
Issue number1
DOIs
StatePublished - Feb 2023

ASJC Scopus subject areas

  • General Mathematics

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