16-25 Konstantin Khanin, Sasa Kocic

Robust local H\"older rigidity of circle maps with breaks (589K, pdf) Mar 13, 16

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Abstract. We prove that, for every $\epsilon\in(0,1)$, every two $C^{2+lpha}$-smooth $(lpha>0)$ circle diffeomorphisms with a break point, i.e. circle diffeomorphisms with a single singular point where the derivative has a jump discontinuity, with the same irrational rotation number $ ho\in(0,1)$ and the same size of the break $c\in\Rr_+ackslash\{1\}$, are conjugate to each other via a conjugacy which is $(1-\epsilon)$-H\"older continuous at the break points.

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