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Browsing by Author "Cilingir, Figen"

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    Fractals Arising From Newton'S Method
    (Amer inst Physics, 2012) Cilingir, Figen; Çilingir, Figen; Matematik
    We consider the dynamics as a special class of rational functions that are obtained from Newton's method when applied to a polynomial equation. Finding solutions of these equations leads to some beautiful images in complex functions. These images represent the basins of attraction of roots of complex functions. We seek the answer "What is the dynamics near the chosen parabolic fixed points?". In addition, we will provide a detailed history of Fractal and Dynamical System Theory.
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    On Newton's method applied to real polynomials
    (Taylor & Francis Ltd, 2012) Cilingir, Figen; Çilingir, Figen; Jarque, Xavier; Matematik
    It is known that if we apply Newton's method to the complex function F(z) = P(z)e(Q(z)), with deg(Q) > 2, then the immediate basin of attraction of the roots of P has finite area. In this paper, we show that under certain conditions on the polynomial P, if deg(Q) = 1, then there is at least one immediate basin of attraction having infinite area.