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Çilingir, Figen

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Yrd. Doç. Dr.
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cilingir@cankaya.edu.tr
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Matematik
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Former Staff
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Scholarly Output

4

Articles

6

Citation Count

2

Supervised Theses

0

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2012 - 20144
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Now showing 1 - 4 of 4
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    Article
    Checkerboard Julia sets for rational maps
    (World Scientific Publ., 2013) Çilingir, Figen; Çilingir, Figen; Cuzzocreo, Daniel; Devaney, Robert L.; Look, Daniel M.; Russell, Elizabeth D.; Matematik
    In this paper, we consider the family of rational maps F-lambda(z) = z(n) + lambda/z(d), where n >= 2, d >= 1, and lambda is an element of C. We consider the case where lambda lies in the main cardioid of one of the n - 1 principal Mandelbrot sets in these families. We show that the Julia sets of these maps are always homeomorphic. However, two such maps F-lambda and F-mu are conjugate on these Julia sets only if the parameters at the centers of the given cardioids satisfy mu = nu(j(d+1))lambda or mu = nu(j(d+1))(lambda) over bar where j is an element of Z and nu is an (n - 1)th root of unity. We define a dynamical invariant, which we call the minimal rotation number. It determines which of these maps are conjugate on their Julia sets, and we obtain an exact count of the number of distinct conjugacy classes of maps drawn from these main cardioids.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 2
    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.
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    Article
    Dağılım fonksiyonlarının yinelenmis fonksiyon sistemleri ile tahmini
    (2014) Çilingir, Figen; 18416; Matematik
    Bir dağılım fonksiyonunun parametrik olmayan tahmin edicisi yinelenmis fonksiyon sistemleri kullanılarak elde edilebilmektedir. Bu yönteme göre, bir dağılım fonksiyonunun tahmin edicisi, (X1, X2,…,Xn) örneklemine bağlı olan bir p parametre vektörü ve w afin dönüsümleri ailesine göre tanımlanan T daralma operatörünün bir sabit noktası olarak düsünülmektedir. Döviz kuru verisi üzerinde yapılan uygulamadan elde edilen sonuçlar bir örnek olarak gösterilmistir.
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    Conference Object
    Citation - WoS: 0
    Citation - Scopus: 0
    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.