17-14 Konstantin Khanin, Sasa Kocic
On the smoothness of the conjugacy for circle maps with a break (524K, PDF) Feb 1, 17
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Abstract. For any $lpha\in(0,1)$, $c\in\Rr_+ackslash\{1\}$ and $\gamma>0$, and Lebesgue almost all irrational $ho\in(0,1)$, any two $C^{2+lpha}$-smooth circle diffeomorphisms with a break, with the same rotation number $ho$ and the same size of the breaks $c$, are conjugate to each other, via a $C^1$-smooth conjugacy whose derivative is uniformly continuous with modulus of continuity $\omega(x)=A|\log x|^{-\gamma}$, for some $A>0$.

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