14-13 Sasa Kocic

Generic rigidity for circle diffeomorphisms with breaks (574K, Pdf) 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 $C^{r-1-arkappa}$-rigid, for any $arkappa>0$.

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