Figen ÇİLİNGİR

23991

Singular Perturbations of Multibrot Set Polynomials

Singular Perturbations of Multibrot Set Polynomials

We will give a complete description of the dynamics of the rational map $N_{F_{M_c}}(z)=\frac{3z^4-2z^3+c}{4z^3-3z^2+c}$ where c is a complex parameter. These are rational maps $N_{F_{M_c}}$ arising from Newton's method. The polynomial of Newton iteration function is obtained from singularly perturbed of the Multibrot set polynomial.
Keywords:

Newton basin, Rational iteration, Julia set Perturbation,

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  • [1] M. H. Holmes, Introduction to Perturbation Methods, Springer, 1995.
  • [2] F. Verhulst, Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, Springer, 2005.
  • [3] M. H. Holmes, Introduction to Perturbation Methods, Springer, 1995.
  • [4] R. L. Devaney, A First Course In Chaotic Dynamical Systems: Theory and Experiment, Second Edition, CRC Press, Taylor and Francis Group, 2020.
  • [5] L. Keen, Julia sets, Chaos and Fractals, the Mathematics behind the Computer Graphics, ed. Devaney and Keen, Proc. Symp. Appl. Math., 39, Amer. Math. Soc., (1989), 57-75.
  • [6] G. Julia, Memoire Sur l’it´eration des functions rationelles, J. Math. Pures Appl., 8 (1918), 47-245. See also Oeuvres de Gaston Julia, Gauthier-Villars, Paris, 1 (1918), 121-319.
  • [7] J. H. Hubbard, B. B. Hubbard, Vector Calculus Linear Algebra, and Differential Forms, Prentice Hall. Upper Saddle River, New Jersey, 07458, 1990.
  • [8] A. Beardon, Iteration of Rational Functions, Springer-Verlag, 1991.
Universal Journal of Mathematics and Applications-Cover
  • ISSN: 2619-9653
  • Başlangıç: 2018
  • Yayıncı: Emrah Evren KARA
Arşiv
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