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arXiv · 2112.05845

Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers

Igors Gorbovickis·Michael Yampolsky
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Abstract

We prove that if two analytic multicritical circle maps with the same bounded type rotation number are topologically conjugate by a conjugacy which matches the critical points of the two maps while preserving the orders of their criticalities, then the conjugacy necessarily has $C^{1+\alpha}$ regularity, where $\alpha$ depends only on the bound on the type of the rotation number. We then extend this rigidity result to $C^3$-smooth bi-cubic circle maps.

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Igors Gorbovickis, Michael Yampolsky. 2021-12-10. Rigidity of analytic and smooth bi-cubic multicritical circle maps with bounded type rotation numbers. https://arxiv.org/abs/2112.05845

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