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Herman’s theory revisited. (English) Zbl 1179.37059
Authors’ abstract: We prove that a C 2+α -smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class D δ ,0δ<α1,α-δ1, is C 1+α-δ -smoothly conjugate to a rigid rotation. This is the first sharp result on the smoothness of the conjugacy. We also derive the most precise version of Denjoy’s inequality for such diffeomorphisms.

MSC:
37E10Maps of the circle
References:
[1]Arnold, V.I.: Small denominators. I. Mapping the circle onto itself. Izv. Akad. Nauk SSSR Ser. Mat. 25, 21–86 (1961) (in Russian)
[2]de Melo, W., van Strien, S.: A structure theorem in one-dimensional dynamics. Ann. Math. (2) 129(3), 519–546 (1989) · Zbl 0737.58020 · doi:10.2307/1971516
[3]Herman, M.-R.: Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. IHES Publ. Math. 49, 5–233 (1979)
[4]Katznelson, Y., Ornstein, D.: The differentiability of the conjugation of certain diffeomorphisms of the circle. Ergod. Theory Dyn. Syst. 9(4), 643–680 (1989)
[5]Katznelson, Y., Ornstein, D.: The absolute continuity of the conjugation of certain diffeomorphisms of the circle. Ergod. Theory Dyn. Syst. 9(4), 681–690 (1989)
[6]Khanin, K.M., Sinai, Y.G.: A new proof of M. Herman’s theorem. Commun. Math. Phys. 112(1), 89–101 (1987) · Zbl 0628.58021 · doi:10.1007/BF01217681
[7]Sinai, Ya.: Topics in Ergodic Theory. Princeton Univ. Press, Princeton (1994)
[8]Sinai, Ya.G., Khanin, K.M.: Smoothness of conjugacies of diffeomorphisms of the circle with rotations. Usp. Mat. Nauk 44(1), 57–82 (1989) (in Russian); English transl., Russ. Math. Surv. 44(1), 69–99 (1989)
[9]Światek, G.: Rational rotation numbers for maps of the circle. Commun. Math. Phys. 119(1), 109–128 (1988) · Zbl 0656.58017 · doi:10.1007/BF01218263
[10]Teplinsky, A.: On cross-ratio distortion and Schwartz derivative. Nonlinearity 55(12), 2777–2783 (2008) · Zbl 05382391 · doi:10.1088/0951-7715/21/12/003
[11]Teplinsky, O.Yu.: On the smoothness of conjugation of circle diffeomorphisms with rigid rotations. Ukr. Math. J. 60(2), 268–282 (2008) (in Ukrainian); English transl.: Ukr. Math. J. 60(2), 310–326 (2008)
[12]Yoccoz, J.-C.: Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne. Ann. Sci. Ecole Norm. Sup. (4) 17(3), 333–359 (1984)
[13]Yoccoz, J.-C.: Il n’y a pas de contre-exemple de Denjoy analytique. C. R. Acad. Sci. Paris Sér. I Math. 298(7), 141–144 (1984)
[14]Yoccoz, J.-C.: Théorème de Siegel, nombres de Bruno et polynômes quadratiques. Astérisque 231, 3–88 (1995)