Abstract
For any α ∈ (0, 1), c ∈ ℝ+ \ {1} and γ > 0 and for Lebesgue almost all irrational ρ ∈ (0, 1), any two C 2+α-smooth circle diffeomorphisms with a break, with the same rotation number ρ and the same size of the breaks c, are conjugate to each other via a C 1-smooth conjugacy whose derivative is uniformly continuous with modulus of continuity ω(x) = A|log x|−γ for some A > 0.
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 297, pp. 224–231.
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Khanin, K., Kocić, S. On the smoothness of the conjugacy between circle maps with a break. Proc. Steklov Inst. Math. 297, 200–207 (2017). https://doi.org/10.1134/S0081543817040125
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DOI: https://doi.org/10.1134/S0081543817040125