Let f be an orientation-preserving circle diffeomorphism with irrational rotation number and with a break point ξ 0 , that is, its derivative f ′ has a jump discontinuity at this point. Suppose that f ′ satisfies a certain Zygmund condition dependent on a parameter γ > 0. We prove that the renormalizations of f are approximated by Möbius transformations in C 1 -norm if γ ∈ (0, 1] and they are approximated in C 2 -norm if γ ∈ (1, +∞). It is also shown, that the coefficients of Möbius transformations get asymptotically linearly dependent.

No abstract

No abstract

No abstract

No abstract