Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME PROPERTIES OF THE JULIA SETS OF QUADRATIC RATIONAL MAPS

  • Received : 2007.02.12
  • Accepted : 2007.03.15
  • Published : 2007.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we give some properties of the dynamics of quadratic rational maps. Using the properties we present the algorithm for drawing the Julia sets of the quadratic rational maps. We illustrate that they are fractals by computer graphics.

Keywords

References

  1. Y. Ahn, A characterizaion of Mandelbrot set of quadratic rational maps, Honam Mathematical J. 27: 405-429, (2005).
  2. A. F. Beardon, Iteration of Rational Functions, Springer-Velag, New York, 1991.
  3. A. Douady and J. Hub-bard, Iteration des polynomes quadratiques complexes, C. R. Acad. Sci. Paris 294 (1982), 123-126.
  4. A. Douady, Sysdynamiques holomorphes, Asterisque 105-106 (1982), 39-63.
  5. P. Fatou, Sur les equations fonctionnelles, Bull. Soc. Math. France 47 (1919), 161-271.
  6. J. D. Foley, A. van Dam, S. K. Feiner and J. F. Hughes, Computer Graphics, Addsion Wesley, Menlo Park (1990).
  7. L. Goldberg and L. keen, The mapping class group of a generic quadratic rational map and automorphisms of the 2-shift, invent. Math. 101 (1990), 335-372. https://doi.org/10.1007/BF01231505
  8. B. Mandelbrot, On the dynamics of iterated maps. Ed. Y. Kuramoto, New York, 1984.
  9. J. Milnor, Geometry and dynamics of quadratic rational maps. Experimental Mathematics, 2, 37-83.
  10. H. O. Peitgen and P. H. Richter, The Beauty of Fractals, Springer-Velag, New York, 1986.
  11. D. Sullivan, Conformal homeomorphisms and dynamics I: Solution of the Fatou-Julia problem on wandering domains, Ann. Math. (1985), 401-418.
  12. Y. Yin, On the Julia sets of quadratic rational maps, Complex Variables 18 (1992), 141-147. https://doi.org/10.1080/17476939208814540