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On \(C^2\)-diffeomorphisms of the circle which are of type III\(_1\). (English) Zbl 0506.58019

MSC:
37A99 Ergodic theory
28D10 One-parameter continuous families of measure-preserving transformations
57R50 Differential topological aspects of diffeomorphisms
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References:
[1] Herman, M.R.: Construction de diffeomorphismes ergodiques. Preprint, (1979)
[2] Herman, M.R.: Sur la conjugaison differentiable des diffeomorphismes du cercle a des rotations. Publ. I.H.E.S.49, 5-234 (1979)
[3] Herman, M.R.: Sur les diffeomorphismes du cercle de nombre de rotation de type constant. Preprint, (1981)
[4] Katznelson, Y.: Sigma-finite invariant measures for smooth mappings of the circle. J. d’Analyse Math.31, 1-18 (1977) · Zbl 0346.28012 · doi:10.1007/BF02813295
[5] Krieger, W.: On the Araki-Woods asymptotic ratio set and non-singular transformations of a measure space. In: Lecture Notes in Mathematics, Vol. 160, pp. 158-177, Berlin-Heidelberg-New York: Springer 1970 · Zbl 0213.34103
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