A Properties of Mandelbrot Set of Quartic Rational Maps

Authors

  • Wisam Ghafil
  • Hussein J. AbdulHussein

DOI:

https://doi.org/10.32792/jeps.v12i2.206

Keywords:

Mandelbrot set, Julia set, Quartic rational maps

Abstract

We present some properties the Mandelbrot set of Quartic rational maps. Every Quartic rational
functions is conjugate to????????+c or λ(????????+1/z+b). We study the Mandelbrot set ????????, the set of parramrters b
for which the Julia set of λ(????????+1/z+b) is connected

References

Pierre Fatou. Sur les equations fonctionnelles.´ Bulletin de la Societ´ e math´ ematique de

France´ , 47:161–271, 1919.

Dennis Sullivan. Quasiconformal homeomorphisms and dynamics i. solution of the

fatoujulia problem on wandering domains. Annals of mathematics, 122(2):401–418, 1985.

Adrien Douady, John Hamal Hubbard, and P Lavaurs. Etude dynamique des polynomesˆ

complexes. 1984.

Benoit B Mandelbrot, Carl JG Evertsz, and Martin C Gutzwiller. Fractals and chaos: the

Mandelbrot set and beyond, volume 3. Springer, 2004.

Tan Lei. Similarity between the mandelbrot set and julia sets. Communications in

mathematical physics, 134(3):587–617, 1990.

Ashish Negi and Mamta Rani. Midgets of superior mandelbrot set. Chaos, Solitons &

Fractals, 36(2):237–245, 2008.

Ahmed F Abdel Jalil and Ayad R Khudair. Toward solving fractional differential

equations via solving ordinary differential equations. Computational and Applied

Mathematics, 41(1):1– 12, 2022.

Alaa Jabbar Badday and Akil J Harfash. Stability of darcy thermosolutal convection in

bidispersive porous medium with reaction. Asia-Pacific Journal of Chemical Engineering,

(5):e2682, 2021.

Young-Joon Ahn. Some properties of the julia sets of quadratic rational maps. Honam

Mathematical Journal, 29(2):205–212, 2007.

SJ Lomonaco. Shor’s quantum factoring algorithm. In Proceedings of Symposia in

Applied Mathematics, volume 58, pages 161–180, 2002.

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Published

2023-02-14