A Sufficient Condition for the Absolute Continuity of Conjugation Between Circle Homeomorphisms With Breaks

Abstract

Let T 1 and T 2 be circle homeomorphisms with countable many break points, that is, discontinuities in the derivative T 1 and T 2 , with identical irrational rotation number ρ. Assume that the total variations of log DT i , i = 1, 2 are bounded. We provide a sufficient condition for the absolute continuity of conjugation between T 1 and T 2. The result extends and complements previous obtained results in [2] and [6].