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The Polynomials Associated with a Julia Set
Bulletin of the London Mathematical Society, 1995Let \(J\) be the Julia set of some polynomial. The authors show that, except in the case when \(J\) is a circle or straight line, then the set of all polynomials which have \(J\) for their Julia set is given by \(\{\sigma p^n,n \in \mathbb{N}, \sigma \in \Sigma\}\) where \(p\) is one of these polynomials with lowest degree, \(\Sigma\) is the set of ...
Schmidt, W., Steinmetz, N.
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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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Mathematische Annalen, 2006
Let \(H:\mathbb{C}^2\longrightarrow \mathbb{C}^2\) be a (complex) Hénon mapping of the form \(H=H_1\circ\cdots\circ H_n\), where \(n\geq 1\), \(H_i(z,w)=(P_i(z)+a_iw,b_iz)\) in which \(P_i\) is a polynomial of degree at least \(2\) and \(a_i\), \(b_i\) are nonzero complex constants. Associated to each Hénon mapping there is a natural invariant measure \
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Let \(H:\mathbb{C}^2\longrightarrow \mathbb{C}^2\) be a (complex) Hénon mapping of the form \(H=H_1\circ\cdots\circ H_n\), where \(n\geq 1\), \(H_i(z,w)=(P_i(z)+a_iw,b_iz)\) in which \(P_i\) is a polynomial of degree at least \(2\) and \(a_i\), \(b_i\) are nonzero complex constants. Associated to each Hénon mapping there is a natural invariant measure \
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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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