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About C 1-minimality of the hyperbolic Cantor sets

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Abstract

In this work we prove that a C 1+α-hyperbolic Cantor set contained in S 1 that is close to an affine Cantor set is not C 1-minimal.

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References

  1. A. Denjoy. Sur les courbes défines par les équations différentielles à la surface du tore. J. de Math Pure et Appl. (9), 11 (1932), 333–375.

    Google Scholar 

  2. M. Herman. Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (French) Inst. Hautes Études Sci. Publ. Math., 49 (1979), 5–233.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Iglesias and A. Portela. On the minimality of locally similar Cantor sets of S 1. Nonlinearity, 22(9) (2009), 2151–2159.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Iglesias and A. Portela. Dynamically defined Cantor sets under the conditions of McDuff’ s conjecture. Colloq. Math., 120(2) (2010), 311–317.

    Article  MathSciNet  MATH  Google Scholar 

  5. A.N. Kercheval. Denjoy minimal sets are far from affine. Ergod. Th. & Dynam. Sys., 22 (2002), 1803–1812.

    Article  MathSciNet  MATH  Google Scholar 

  6. A.N. Kercheval. Erratum for Denjoy minimal sets are far from affine, http://www.math.fsu.edu/ kercheva/papers/.

  7. B. Kra and J. Schmeling. Diophantine classes, dimension and Denjoy maps. Acta Arith., 105(4) (2002), 323–340.

    Article  MathSciNet  MATH  Google Scholar 

  8. D. McDuff. C 1-minimal subset of the circle. Ann. Inst. Fourier, Grenoble, 31 (1981), 177–193.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Portela. Regular Interval Cantor sets of S 1 and minimality. Bulletin of the BrazilianMathematical Society, New Series, 40(1) (2009), 53–75.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Centro de Ciências Exatas e de Tecnologia, Departamento de Matemática, Fundação Universidade Federal de São Carlos, Rod. Washington Luís, Km 235, C.P. 676, 13565-905, São Carlos, Brasil

    Liane Bordignon

  2. Instituto de Matemática, Facultad de Ingeniería, Universidad de la Republica, CC30, CP 11300, Montevideo, Uruguay

    Jorge Iglesias & Aldo Portela

Authors
  1. Liane Bordignon
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  2. Jorge Iglesias
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  3. Aldo Portela
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Corresponding author

Correspondence to Jorge Iglesias.

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Cite this article

Bordignon, L., Iglesias, J. & Portela, A. About C 1-minimality of the hyperbolic Cantor sets. Bull Braz Math Soc, New Series 45, 525–542 (2014). https://doi.org/10.1007/s00574-014-0061-y

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  • DOI: https://doi.org/10.1007/s00574-014-0061-y

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