Research Article

Singular Perturbations of Multibrot Set Polynomials

Volume: 5 Number: 4 December 29, 2022
EN

Singular Perturbations of Multibrot Set Polynomials

Abstract

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

Supporting Institution

Bu makale " The first International Karatekin Science and Technology Conference that held on September 1-3, 2022 " konferansına hazırlanan sunumdan elde edilen sonuçlarla ortaya çıkmıştır. Destekleyen herhangi bir kurum yoktur.

Thanks

The first International Karatekin Science and Technology Conference that held on September 1-3, 2022 konferansı düzenleyen hocalarımıza teşekkür ederim. Ayrıca editöre destek ve yarımları için teşekkür ederim.

References

  1. [1] M. H. Holmes, Introduction to Perturbation Methods, Springer, 1995.
  2. [2] F. Verhulst, Methods and Applications of Singular Perturbations: Boundary Layers and Multiple Timescale Dynamics, Springer, 2005.
  3. [3] M. H. Holmes, Introduction to Perturbation Methods, Springer, 1995.
  4. [4] R. L. Devaney, A First Course In Chaotic Dynamical Systems: Theory and Experiment, Second Edition, CRC Press, Taylor and Francis Group, 2020.
  5. [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. [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. [7] J. H. Hubbard, B. B. Hubbard, Vector Calculus Linear Algebra, and Differential Forms, Prentice Hall. Upper Saddle River, New Jersey, 07458, 1990.
  8. [8] A. Beardon, Iteration of Rational Functions, Springer-Verlag, 1991.
APA
Çilingir, F. (2022). Singular Perturbations of Multibrot Set Polynomials. Universal Journal of Mathematics and Applications, 5(4), 130-135. https://doi.org/10.32323/ujma.1174056
AMA
1.Çilingir F. Singular Perturbations of Multibrot Set Polynomials. Univ. J. Math. Appl. 2022;5(4):130-135. doi:10.32323/ujma.1174056
Chicago
Çilingir, Figen. 2022. “Singular Perturbations of Multibrot Set Polynomials”. Universal Journal of Mathematics and Applications 5 (4): 130-35. https://doi.org/10.32323/ujma.1174056.
EndNote
Çilingir F (December 1, 2022) Singular Perturbations of Multibrot Set Polynomials. Universal Journal of Mathematics and Applications 5 4 130–135.
IEEE
[1]F. Çilingir, “Singular Perturbations of Multibrot Set Polynomials”, Univ. J. Math. Appl., vol. 5, no. 4, pp. 130–135, Dec. 2022, doi: 10.32323/ujma.1174056.
ISNAD
Çilingir, Figen. “Singular Perturbations of Multibrot Set Polynomials”. Universal Journal of Mathematics and Applications 5/4 (December 1, 2022): 130-135. https://doi.org/10.32323/ujma.1174056.
JAMA
1.Çilingir F. Singular Perturbations of Multibrot Set Polynomials. Univ. J. Math. Appl. 2022;5:130–135.
MLA
Çilingir, Figen. “Singular Perturbations of Multibrot Set Polynomials”. Universal Journal of Mathematics and Applications, vol. 5, no. 4, Dec. 2022, pp. 130-5, doi:10.32323/ujma.1174056.
Vancouver
1.Figen Çilingir. Singular Perturbations of Multibrot Set Polynomials. Univ. J. Math. Appl. 2022 Dec. 1;5(4):130-5. doi:10.32323/ujma.1174056