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On absolute continuity of conjugations between circle maps with break points. (English) Zbl 1256.37030

Summary: Let \(T_1\) and \(T_2\) be piecewise smooth circle homeomorphisms with break points and identical irrational rotation numbers. We provide one sufficient and necessary condition for the absolute continuity of the conjugation map between \(T_1\) and \(T_2\).

MSC:

37E10 Dynamical systems involving maps of the circle
37E45 Rotation numbers and vectors
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
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