caa a22 4500 386377855 CHVBK 20180307112028.0 cr unu---uuuuu 161130e198912 xx s 000 0 eng 10.1017/S0143385700005289 doi S0143385700005289 pii (NATIONALLICENCE)cambridge-10.1017/S0143385700005289 The absolute continuity of the conjugation of certain diffeomorphisms of the circle [Elektronische Daten] Let f be an orientation preserving -diffeomorphism of the circle. If the rotation number α = ρ(f) is irrational and log Df is of bounded variation then, by a wellknown theorem of Denjoy, f is conjugate to the rigid rotation Rα. The conjugation means that there exists an essentially unique homeomorphism h of the circle such that f = h−lRαh. The general problem of relating the smoothness of h to that of f under suitable diophantine conditions on α has been studied extensively (cf. [H1], [KO], [Y] and the references given there). At the bottom of the scale of smoothness for f there is a theorem of M. Herman [H2] which states that if Df is absolutely continuous and D log Df Lp, p > 1, α = ρ (f) is of ‘constant type' which means ‘the coefficients in the continued fraction expansion of α are bounded', and if f is a perturbation of Rα, then h is absolutely continuous. Our purpose in this paper is to give a different proof and an improved version of Herman's theorem. The main difference in the result is that we do not need to assume that f is close to Rα; the proof is very different from Herman's and is very much in the spirit of [KO]. Copyright © Cambridge University Press 1989 Katznelson Y. Mathematics Department, Stanford University, Stanford CA 94305, USA Ornstein D. Mathematics Department, Stanford University, Stanford CA 94305, USA Ergodic Theory and Dynamical Systems Cambridge University Press 9/4(1989-12), 681-690 0143-3857 9:4<681 1989 9 ETS https://doi.org/10.1017/S0143385700005289 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0143385700005289 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Katznelson Y. Mathematics Department, Stanford University, Stanford CA 94305, USA NATIONALLICENCE 700 1- Ornstein D. Mathematics Department, Stanford University, Stanford CA 94305, USA NATIONALLICENCE 773 0- Ergodic Theory and Dynamical Systems Cambridge University Press 9/4(1989-12), 681-690 0143-3857 9:4<681 1989 9 ETS CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge