Konstantin Khanin, Sasa Kocic, Elio Mazzeo
C^1-rigidity of circle diffeomorphisms with breaks for almost all rotation numbers
(683K, pdf)

ABSTRACT.  We prove that for almost all rotation numbers, every two $C^{2+lpha}$-smooth circle diffeomorphisms with a break point, with the same irrational rotation number and the same size of the break, are $C^{1}$-smoothly conjugate to each other, provided that the corresponding renormalizations approach asymptotically each other with an exponential rate.