Singular Perturbations of Multibrot Set Polynomials

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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.