Hiroshima Mathematical Journal

On the Julia sets of rational functions of degree two with two real parameters

Toshio Nakata and Munetaka Nakamura

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 26, Number 2 (1996), 253-275.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206127360

Digital Object Identifier
doi:10.32917/hmj/1206127360

Mathematical Reviews number (MathSciNet)
MR1400539

Zentralblatt MATH identifier
0903.30021

Subjects
Primary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
Secondary: 58F25

Citation

Nakata, Toshio; Nakamura, Munetaka. On the Julia sets of rational functions of degree two with two real parameters. Hiroshima Math. J. 26 (1996), no. 2, 253--275. doi:10.32917/hmj/1206127360. https://projecteuclid.org/euclid.hmj/1206127360


Export citation

References

  • [1] A. Beardon, Iteration of Rational Functions, Springer-Verlag, GTM132, (1991).
  • [2] R. Devaney, An introduction to chaotic dynamical systems, second edition, Addison Wesley Publishing Company Inc, (1989).
  • [3] K. Falconer, The geometry of fractal sets, Cambridge Univ Press, (1985).
  • [4] K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, John Willey and Sons, (1990).
  • [5] M. Lyubich, Dynamics of rational transformations: topological picture, Russ. Math. Surv., 41 (1986), 43-117.
  • [6] J. Milnor, Dynamics in One Complex Variable: Introductory Lectures (1990), SUNY Stony Brook Institute for Mathematical Sciences Preprint, #1990/5.
  • [7] M. Rees, Components of degree two hyperbolic rational maps, Invent. Math., 100 (1990), 357-382.
  • [8] D. Ruelle, Repellers for real analytic maps, Ergod. Th. and Dynam. Sys., (1982), 2:99-108.
  • [9] N. Saito, S. Sait, and A. Shimizu, An Analysis of a Family of Rational Maps which Contains Integrable and Nonintegrable Difference Analogue of the Logistic Equation, Preprint, 1993.