K. Khanin, S. Kocic Renormalization conjecture and rigidity theory for circle diffeomorphisms with breaks (673K, PDF) ABSTRACT. We prove the renormalization conjecture for circle diffeomorphisms with breaks, i.e. that the renormalizations of any two $C^{2+lpha}$-smooth circle diffeomorphisms with a break point, with the same irrational rotation number and the same size of the break, approach each other exponentially fast in the $C^2$-topology. As a corollary, we obtain the following rigidity result: for almost all irrational rotation numbers, any two circle diffeomorphisms with a break, with the same rotation number and the same size of the break, are $C^1$-smoothly conjugate to each other.