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Applied Mathematics and Computation, 2023
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Buried components of a julia set
Applied Mathematics-A Journal of Chinese Universities, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sun, Yeshun, Yang, Chungchun
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International Journal of Bifurcation and Chaos, 2008
The goal of this paper is to investigate the iterative behavior of a particular class of rational functions which arise from Newton's method applied to the entire function (z2 + c)eQ(z) where c is a complex parameter and Q is a nonconstant polynomial with deg(Q) ≤ 2. In particular, the basins of attracting fixed points will be described.
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The goal of this paper is to investigate the iterative behavior of a particular class of rational functions which arise from Newton's method applied to the entire function (z2 + c)eQ(z) where c is a complex parameter and Q is a nonconstant polynomial with deg(Q) ≤ 2. In particular, the basins of attracting fixed points will be described.
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Julia sets and Mandelbrot sets in Noor orbit
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ashish, Mamta Rani, Renu Chugh
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JULIA AND MANDELBROT SETS OF CHEBYSHEV FAMILIES
International Journal of Bifurcation and Chaos, 2001We present one-parameter families of rational functions of arbitrary degree d which are globally generalized polynomial-like of degree d and roughly speaking locally quadratic-like everywhere, where the parameter appears not only as a purely multiplicative factor but also in a more complicated nonlinear way.
Franz Peherstorfer, Christoph Stroh
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Julia Sets and the Mandelbrot Set
1986Quadratic Julia sets, and the Mandelbrot set, arise in a mathematical situation which is extremely simple, namely from sequences of complex numbers defined inductively by the relation $$z_n + = z_n^2 + c,$$ where c is a complex constant. I must say that, in 1980, whenever I told my friends that I was just starting with J.H.
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Visual Explanation of the Complexity in Julia Sets
Computer Graphics Forum, 2013AbstractJulia sets based on quadratic polynomials have a very simple definition, yet a highly intricate shape. Our contribution is to provide a visual explanation for this complexity. To this end we show the construction of Julia sets as a dynamic process, in contrast to showing just a static image of the set itself.
Schrijvers, O.J., Wijk, van, J.J.
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Julia sets of switched processes
Computers & Graphics, 1991Abstract Julia sets of switched processes are introduced. Such processes are of importance in the study of dynamical systems in which several free-standing processes may be involved.
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Elliptic Functions with Disconnected Julia Sets
International Journal of Bifurcation and Chaos, 2016In this paper, we investigate elliptic functions of the form [Formula: see text], where [Formula: see text] is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin and five other equivalence classes of critical points.
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The JuliaConnectoR: A Functionally-Oriented Interface for Integrating Julia in R
Journal of Statistical Software, 2022Stefan Lenz +2 more
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