Singular Perturbations of Multibrot Set Polynomials

Authors : Figen Çilingir

Pages : 130-135

Doi:10.32323/ujma.1174056

View : 18 | Download : 11

Publication Date : 2022-12-29

Article Type : Research

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