Convergence of renormalizations of circle homeomorphisms with breaks

Consider the circle homeomorphisms with a break point and satisfying Katznelson and Ornstein smoothness conditions. Renormalizations of such maps with irrational rotation number, approximated by fractional-linear maps in $C^{1+L_1}$-norm. In addition, renormalizations of two circle homeomorphisms with the same irrational rotation number of bounded type and with the same size of break, converge to each other in $C^{1+L_1}$-norm.