Rigidity and renormalization for circle diffeomorphisms with breaks

The talk focuses on presenting recent findings regarding the convergence of renormalizations and the rigidity of circle diffeomorphisms having break-type singularities. Specifically, it demonstrates that two such circle diffeomorphisms, having identical characteristics such as the same irrational rotation number of bounded type, the same size of break, and satisfying certain Zygmund conditions, can be smoothly conjugated.