David regularity of the Yoccoz extension

Luna Lomonaco; Lucas Oliveira; Miguel Ratis Laude

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arXiv · 2411.08643

David regularity of the Yoccoz extension

Luna Lomonaco·Lucas Oliveira·Miguel Ratis Laude

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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.

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Luna Lomonaco, Lucas Oliveira, Miguel Ratis Laude. 2024-11-13. David regularity of the Yoccoz extension. https://arxiv.org/abs/2411.08643

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