Skip to main content
SpringerLink
Log in

Symbolic dynamics for angle-doubling on the circle I. The topology of locally connected Julia sets

  • Conference paper
  • First Online:
Ergodic Theory and Related Topics III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1514))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bandt, C. and Keller, K., Self-similar sets 2. A simple approach to the topological structure of fractals. Math. Nachr., to appear

    Google Scholar 

  2. Bandt, C. and Keller, K., Symbolic dynamics for angle-doubling on the circle, II. Description of the abstract Mandelbrot set. Preprint, Greifswald 1991

    Google Scholar 

  3. Blanchard, P., Complex analytic dynamics on the Riemann sphere. Bull. Amer. Math. Soc. 11 (1984), 85–141.

    Article  MathSciNet  MATH  Google Scholar 

  4. Branner, B. and Hubbard, J.H., The iteration of cubic polynomials. Part 1: The global topology of parameter space. Acta Math. 160 (1988), 143–206.

    Article  MathSciNet  MATH  Google Scholar 

  5. Collet, P. and Eckmann, J.-P., Iterated maps on the interval as dynamical systems. Birkhäuser 1980.

    Google Scholar 

  6. Douady, A. and Hubbard, J. Étude dynamique des polynômes complexes, Première partie. Publications Mathématiques d’Orsay, 1984.

    Google Scholar 

  7. Douady, A. and Hubbard, J. On the dynamics of polynomial-like mappings. Ann. Sci. Ecole Norm. Sup. (4), 18 (1985), 287–343.

    MathSciNet  MATH  Google Scholar 

  8. Hubbard, J.H., according to J.-C. Yoccoz. Puzzles and quadratic tableaux. Preprint, Paris 1990.

    Google Scholar 

  9. Kuratowski, K. Topology, Vol. 1, 2, New York and Warszawa 1966,1968.

    Google Scholar 

  10. Lavaurs, P. Une déscription combinatoire de l’involution définie par M sur les rationnels à dénominateur impair. C. R. Acad. Sc. Paris Série I, t. 303 (1986), 143–146

    MathSciNet  MATH  Google Scholar 

  11. Lyubich, M. Yu. Dynamics of rational transformations: topological picture. Uspekhi Mat. Nauk 41 (1986) no. 4 (250), 35–95, 239.

    MathSciNet  Google Scholar 

  12. Milnor, J. and Thurston, W.P. On iterated maps of the interval, Lecture Notes in Mathematics 1342 (1988), 465–563.

    Article  MathSciNet  MATH  Google Scholar 

  13. Rees, M. A partial description of parameter space of rational maps of degree two: Part 1. Acta Math., to appear

    Google Scholar 

  14. Sullivan, D. Quasiconformal homeomorphisms and dynamics I. Solution of the Fatou-Julia problem on wandering domains, Annals Math. 122 (1985), 401–418.

    Article  MathSciNet  MATH  Google Scholar 

  15. Thurston, W.P. On the combinatorics and dynamics of iterated rational maps. Preprint, Princeton 1985.

    Google Scholar 

  16. Penrose, C. On quotients of the shift associated with dendrite Julia sets of quadratic polynomials. Thesis, Warwick 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Ernst-Moritz-Arndt-Universität, D-O-2200, Greifswald, Germany

    Christoph Bandt & Karsten Keller

Authors
  1. Christoph Bandt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karsten Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Ulrich Krengel Karin Richter Volker Warstat

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Bandt, C., Keller, K. (1992). Symbolic dynamics for angle-doubling on the circle I. The topology of locally connected Julia sets. In: Krengel, U., Richter, K., Warstat, V. (eds) Ergodic Theory and Related Topics III. Lecture Notes in Mathematics, vol 1514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097524

Download citation

  • DOI: https://doi.org/10.1007/BFb0097524

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55444-8

  • Online ISBN: 978-3-540-47076-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation