Low Smoothness: Renormalizations of circle maps with rational rotation numbers again behave as Möbius functions
Consider a one-parameter family of circle maps f t = f 0 + t(mod1), where f 0 is
a circle homeomorphism with two break points. Suppose Df 0 satisfies a certain Zygmund type
smoothness condition depending on a parameter γ > 0. We prove that the renormalizations of
circle homeomorphisms from this family with rational rotation number of sufficiently large rank are
approximated by Mobius functions in C 1+L 1 -norm if γ ∈ (1/2,1] and in C 2 -norm if γ > 1.
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