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On rigidity of critical circle maps

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Abstract

We give examples of analytic critical circle maps which are not C 1+α rigid.

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References

  1. E. de Faria and W. de Melo. Rigidity of critical circle mappings. I.J. Eur. Math. Soc. (JEMS), 1(4) (1999), 339–392.

    Article  MATH  Google Scholar 

  2. E. de Faria and W. de Melo. Rigidity of critical circle mappings. II. J. Amer.Math. Soc., 13(2) (2000), 343–370.

    Article  MATH  Google Scholar 

  3. K. Khanin and A. Teplinsky. Robust rigidity for circle diffeomorphisms with singularities. Invent. Math., 169 (2007), 193–218.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. Khmelev and M. Yampolski. Rigidity problem for analytic critical circle maps. Moscow Math. Journ., 6 (2006), 317–351.

    MATH  Google Scholar 

  5. W. de Melo and S. van Strien. One-dimensional dynamics. Ergebnisse derMathematik und ihrer Grenzgebiete (3), 25 (1993), xiv+605 pp. Springer-Verlag, Berlin.

  6. J-C Yoccoz. Il n’y a pas de contre-exemple de Denjoy analytique. C.R. Acad. Sci. Paris Sr. I Math., 298(7) (1984), 141–144.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. CNRS UMR 7586 Institut de Mathématiques de Jussieu Paris Rive Gauche, Bâtiment Sophie Germain, Case 7012, 75205, Paris Cedex 13, France

    Artur Avila

  2. IMPA, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil

    Artur Avila

Authors
  1. Artur Avila
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Correspondence to Artur Avila.

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Avila, A. On rigidity of critical circle maps. Bull Braz Math Soc, New Series 44, 611–619 (2013). https://doi.org/10.1007/s00574-013-0027-5

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  • DOI: https://doi.org/10.1007/s00574-013-0027-5

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