Acta Mathematica

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

Carsten Lunde Petersen

Full-text: Open access

Article information

Source
Acta Math., Volume 177, Number 2 (1996), 163-224.

Dates
Received: 27 June 1994
Revised: 22 May 1996
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890982

Digital Object Identifier
doi:10.1007/BF02392621

Mathematical Reviews number (MathSciNet)
MR1440932

Zentralblatt MATH identifier
0884.30020

Rights
1996 © Institut Mittag-Leffler

Citation

Lunde Petersen, Carsten. Local connectivity of some Julia sets containing a circle with an irrational rotation. Acta Math. 177 (1996), no. 2, 163--224. doi:10.1007/BF02392621. https://projecteuclid.org/euclid.acta/1485890982


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References

  • [Be] Beardon, A. F., Iteration of Rational Functions Graduate Texts in Math., 132. Springer-Verlag, New York-Berlin, 1991.
  • [BH] Branner, B. & Hubbard, J. H., The iteration of cubic polynomials, Part II: Patterns and parapatterns. Acta Math., 169 (1992), 229–325.
  • [CG] Carleson, L. & Gamelin, T. W., Complex Dynamics, Universitext: Tracts in Mathematics Springer-Verlag, New York, 1993.
  • [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, in Topological Methods in Modern Mathematics (Stony Brook, NY 1991), pp. 467–511. Publish or Perish, Houston, TX, 1993.
  • [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.
  • [LV] Lehto, O. & Virtanen, K. I., Quasiconformal Mappings in the Plane, 2nd edition Grundlehren Math. Wiss. 126. Springer-Verlag, New York-Berlin, 1973.
  • [Mc] McMullen, C. T., Self-similarity of Siegel disks and Hausdorff dimension of Julia sets. Manuscript, Univ. of California, Berkeley, CA, October 1995.
  • [Si] Siegel, L., Iteration of analytic functions. Ann. of Math. (2), 43 (1942), 607–612.
  • [St] Steinmetz, N., Rational Iteration. Complex Analytic Dynamical Systems. de Gruyter Stud. Math., 16, de Gruyter, Berlin, 1993.
  • [Su] Sullivan, D., Bounds, quadratic differentials, and renormalization conjectures, in American Mathematical Society Centennial Publications, Vol. II (Providence, RI, 1988), pp. 417–466. Amer. Math. Soc., Providence, RI, 1992.
  • [Sw] Świątec, G., Rational rotation numbers for maps of the circle. Comm. Math. Phys., 119 (1988), 109–128.
  • [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 in Acta 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.
  • [Yo2] Yoccoz, J.-C. Structure des orbites des homéomorphismes analytiques possedant un point critique. Manuscript.