References
Erdös, P.: Representations of real numbers as sums and products of Liouville numbers. Mich. Math. J.9, 59–60 (1962)
Haefliger, A., Banghe, L.: Currents on circle invariant by a Fuchsian group geometric dynamics. In: Palis, J., Jr. (ed.) Geometric dynamics. Proceedings Rio de Janeiro 1981. (Lect. Notes Math., vol. 1007, pp. 369–378) Berlin Heidelberg New York: Springer 1983
Haefliger, A.: Some remarks on foliations with minimal leaves. J. Differ. Geom.15, 269–284 (1980)
Herman, M.R.: Sur la conjugaison différentiable des différentiable des diffeomorphismes de cercle à des rotations. Publ. I.H.E.S.49, 5–233 (1979)
Jarnik, V.: Ueber einen Satz von A. Khinchine, zweite Mitteilung. Acta Arith.2, 1–22 (1936)
Katznelson, Y., Ornstein, D.: The differentiability of the conjugation of certain diffeomorphisms of the circle. Ergodic Theory Dyn. Syst.9, 643–680 (1989)
Khanin, K.M., Sinai, Y.: A new proof of M. Herman's theorem. Commun. Math. Phys. 112, 89–101 (1987)
Moser, J.: A stability theorem for minimal foliations on a torus. Ergodic Theory Dyn. Syst.8, 251–281 (1988)
Schmidt, W.: Diophantine approximations. (Lect. Notes Math., vol. 785), Berlin Heidelberg New York: Springer 1980
Siegel, C.L.: Iteration of analytic functions. Ann. Math.43, 607–612 (1942)
Sprindžuk, V. G.: Metric theory of Diophantine approximations. New York: Wiley 1979
Yoccoz, J.C.: Theses at the Université Paris Sud, in particular lère thèse: Centralisateurs et conjugaison différentiable des diffeomorphismes du cercle, June 1985
Yoccoz, J.C.: Conjugaison différentiable des diffeomorphismes du cercle dont le nombre de rotation vérifie une condition Diophantine. Ann. Sci. Éc. Norm. Supér., IV Sér.17, 333–359 (1984)
Zehnder, E.: Generalized implicit function theorem with applications to small divisor problems I. Commun. Pure Appl. Math.28, 91–140 (1975)
Cartan, H.: Une théorème sur les groupes ordonés. Bull. Sci. Math.63, 201–205 (1939)
Hölder, O.: Die Axiome der Quantität und die Lehre vom Mass. Berichte der Verhandl. der Sächsischen Akad. Wiss., Leipzig52, 1–64 (1901)
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Dedicated in friendship to A. Haefliger
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Moser, J. On commuting circle mappings and simultaneous Diophantine approximations. Math Z 205, 105–121 (1990). https://doi.org/10.1007/BF02571227
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DOI: https://doi.org/10.1007/BF02571227