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Local connectivity of some Julia sets containing a circle with an irrational rotation

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Acta Mathematica

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References

  • [Be]Beardon, A. F.,Iteration of Rational Functions Graduate Texts in Math., 132. Springer-Verlag, New York-Berlin, 1991.

    Google Scholar 

  • [BH]Branner, B. &Hubbard, J. H., The iteration of cubic polynomials, Part II: Patterns and parapatterns.Acta Math., 169 (1992), 229–325.

    MathSciNet  Google Scholar 

  • [CG]Carleson, L. &Gamelin, T. W.,Complex Dynamics, Universitext: Tracts in Mathematics Springer-Verlag, New York, 1993.

    Google Scholar 

  • [Do]Douady, A., Disques de Siegel et anneaux de Herman.Sém. Bourbaki, 39ème année, 1986/87, no 677.

  • [He]Herman, M. R., Conjugaison quasi symmetrique des homéomorphismes analytiques du cercle a des rotations. Preliminary manuscript.

  • [Hu]Hubbard, J. H., Local connectivity of Julia sets and bifurcation loci: three theorems by Yoccoz, inTopological Methods in Modern Mathematics (Stony Brook, NY 1991), pp. 467–511. Publish or Perish, Houston, TX, 1993.

    Google Scholar 

  • [Ke]Keller, K., Symbolic dynamics for angle-doubling on the circle III. Sturmian sequences and the the quadratic map.Ergodic Theory Dynamical Systems, 14, (1994), 787–805.

    MATH  Google Scholar 

  • [LV]Lehto, O. &Virtanen, K. I.,Quasiconformal Mappings in the Plane, 2nd edition Grundlehren Math. Wiss. 126. Springer-Verlag, New York-Berlin, 1973.

    Google Scholar 

  • [Mc]McMullen, C. T., Self-similarity of Siegel disks and Hausdorff dimension of Julia sets. Manuscript, Univ. of California, Berkeley, CA, October 1995.

    Google Scholar 

  • [Si]Siegel, L., Iteration of analytic functions.Ann. of Math. (2), 43 (1942), 607–612.

    Article  MATH  MathSciNet  Google Scholar 

  • [St]Steinmetz, N.,Rational Iteration. Complex Analytic Dynamical Systems. de Gruyter Stud. Math., 16, de Gruyter, Berlin, 1993.

    Google Scholar 

  • [Su]Sullivan, D., Bounds, quadratic differentials, and renormalization conjectures, inAmerican Mathematical Society Centennial Publications, Vol. II (Providence, RI, 1988), pp. 417–466. Amer. Math. Soc., Providence, RI, 1992.

    Google Scholar 

  • [Sw]Świątec, G., Rational rotation numbers for maps of the circle.Comm. Math. Phys., 119 (1988), 109–128.

    Article  MathSciNet  Google Scholar 

  • [TY]Tan, L. & Yin, Y., Local connectivity of the Julia set for geometrically finite rational maps. Preprint, École Normale Supérieure de Lyon, UMPA-94-no 121, 1994. To appear inActa Math. Sinica.

  • [Ya]Yampolsky, M., Complex bounds for critical circle maps. Preprint, SUNY, StonyBrook, Institute for Mathematical Sciences #1995/12.

  • [Yo1]Yoccoz, J.-C., Il n'y a pas de contre-exemple de Denjoy analytique.C. R. Acad. Sci. Paris Sér. I Math., 298 (1984), 141–144.

    MATH  MathSciNet  Google Scholar 

  • [Yo2]Yoccoz, J.-C. Structure des orbites des homéomorphismes analytiques possedant un point critique. Manuscript.

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  1. IMFUA, Roskilde University, Postbox 260, DK-4000, Roskilde, Denmark

    Carsten Lunde Petersen

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  1. Carsten Lunde Petersen
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Lunde Petersen, C. Local connectivity of some Julia sets containing a circle with an irrational rotation. Acta Math. 177, 163–224 (1996). https://doi.org/10.1007/BF02392621

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  • DOI: https://doi.org/10.1007/BF02392621

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