David regularity of the Yoccoz extension

TL;DR

This paper investigates the regularity of Yoccoz extensions of critical circle maps, focusing on when these extensions admit a David extension, thereby advancing understanding of conjugator regularity in circle dynamics.

Contribution

It classifies the David regularity of the Yoccoz extension, providing new insights into the extension process and conjugator regularity in critical circle dynamics.

Findings

Classifies when Yoccoz extensions admit David extensions.

Builds on Petersen and Zakeri's work to analyze extension regularity.

Advances understanding of conjugator regularity in critical circle maps.

Abstract

A central problem in the study of critical circle dynamics is understanding the regularity of Yoccoz conjugators - circle homeomorphisms that conjugate critical circle maps with irrational rotation numbers to their corresponding rigid rotations. One can approach this problem from a different angle by studying the regularity of extensions of these maps to the unit disk. Of particular interest is the question of when such a conjugator admits a David extension. Building on the work of Petersen and Zakeri, we classify the David regularity of a specific extension process known as the Yoccoz extension.