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The rigidity problem for analytic critical circle maps

D. Khmelev·M. Yampolsky
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Abstract

It is shown that if $f$ and $g$ are any two analytic critical circle mappings with the same irrational rotation number, then the conjugacy that maps the critical point of $f$ to that of $g$ has regularity $C^{1+α}$ at the critical point, with a universal value of $α>0$. As a consequence, a new proof of the hyperbolicity of the full renormalization horseshoe of critical circle maps is given.

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D. Khmelev, M. Yampolsky. 2005-02-04. The rigidity problem for analytic critical circle maps. https://arxiv.org/abs/math/0501448

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