 1413 Sasa Kocic
 Generic rigidity for circle diffeomorphisms with breaks
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Mar 17, 14

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Abstract. We prove that $C^r$smooth ($r>2$) circle diffeomorphisms with a break, i.e., circle diffeomorphisms with a single singular point where the derivative has a jump discontinuity, are generically, i.e., for almost all irrational rotation numbers, not $C^{1+arepsilon}$rigid, for any $arepsilon>0$. This result complements our recent proof, joint with K. Khanin, that such maps are generically $C^1$rigid. It stands in remarkable contrast to the result of J.C. Yoccoz that $C^r$smooth circle diffeomorphisms are generically $C^{r1arkappa}$rigid, for any $arkappa>0$.
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