Acta Mathematica

, Volume 177, Issue 2, pp 163–224 | Cite as

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

  • Carsten Lunde Petersen
Article

Keywords

Local Connectivity Irrational Rotation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Be]Beardon, A. F.,Iteration of Rational Functions Graduate Texts in Math., 132. Springer-Verlag, New York-Berlin, 1991.Google Scholar
  2. [BH]Branner, B. &Hubbard, J. H., The iteration of cubic polynomials, Part II: Patterns and parapatterns.Acta Math., 169 (1992), 229–325.MathSciNetGoogle Scholar
  3. [CG]Carleson, L. &Gamelin, T. W.,Complex Dynamics, Universitext: Tracts in Mathematics Springer-Verlag, New York, 1993.Google Scholar
  4. [Do]Douady, A., Disques de Siegel et anneaux de Herman.Sém. Bourbaki, 39ème année, 1986/87, no 677.Google Scholar
  5. [He]Herman, M. R., Conjugaison quasi symmetrique des homéomorphismes analytiques du cercle a des rotations. Preliminary manuscript.Google Scholar
  6. [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
  7. [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.MATHGoogle Scholar
  8. [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
  9. [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
  10. [Si]Siegel, L., Iteration of analytic functions.Ann. of Math. (2), 43 (1942), 607–612.CrossRefMATHMathSciNetGoogle Scholar
  11. [St]Steinmetz, N.,Rational Iteration. Complex Analytic Dynamical Systems. de Gruyter Stud. Math., 16, de Gruyter, Berlin, 1993.Google Scholar
  12. [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
  13. [Sw]Świątec, G., Rational rotation numbers for maps of the circle.Comm. Math. Phys., 119 (1988), 109–128.CrossRefMathSciNetGoogle Scholar
  14. [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.Google Scholar
  15. [Ya]Yampolsky, M., Complex bounds for critical circle maps. Preprint, SUNY, StonyBrook, Institute for Mathematical Sciences #1995/12.Google Scholar
  16. [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.MATHMathSciNetGoogle Scholar
  17. [Yo2]Yoccoz, J.-C. Structure des orbites des homéomorphismes analytiques possedant un point critique. Manuscript.Google Scholar

Copyright information

© Institut Mittag-Leffler 1996

Authors and Affiliations

  • Carsten Lunde Petersen
    • 1
  1. 1.IMFUARoskilde UniversityRoskildeDenmark

Personalised recommendations