Results 31 to 40 of about 64,522 (306)
Limit Directions of Julia Sets of Entire Functions and Complex Differential Equations
Journal of Mathematics, 2023 The limiting directions of Julia sets of infinite order entire functions are studied by combining the theory of complex dynamic system and the theory of complex differential equations, in which the lower bound of the measure of limiting direction of ...
Zhigao Qin, Jianren Long, Xuxu Xiang
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The Geometry of Julia Sets [PDF]
Transactions of the American Mathematical Society, 1993 The long term analysis of dynamical systems inspired the study of the dynamics of families of mappings. Many of these investigations led to the study of the dynamics of mappings on Cantor sets and on intervals. Julia sets play a critical role in the understanding of the dynamics of families of mappings.
Aarts, Jan M., Oversteegen, Lex G.
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Mandelbrot Sets and Julia Sets in Picard-Mann Orbit
IEEE Access, 2020 The purpose of this paper is to introduce the Mandelbrot and Julia sets by using Picard-Mann iteration procedure. Escape criteria is established which plays an important role to generate Mandelbrot and Julia sets.
Cui Zou +4 more
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AIMS Mathematics, 2022 In this paper, we mainly investigate the radial distribution of Julia sets of difference operators of entire solutions of complex differential equation $ F(z)f^{n}(z)+P(z, f) = 0 $, where $ F(z) $ is a transcendental entire function and $ P(z, f) $ is a ...
Jingjing Li, Zhigang Huang
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Julia Sets in Parameter Spaces [PDF]
Communications in Mathematical Physics, 2001 The paper is devoted to study the one parameter family of cubic polynomials \[ g_b(z)= \lambda z+ bz^2+z^3, \quad b\in \mathbb{C},\tag{1} \] where \(\lambda= e^{2\pi i\theta}\) is a fixed complex number of modulus 1. The authors show that the bifurcation locus of (1) contains quasi-conformal copies of the quadratic Julia set \(J(\lambda z+z^2)\).
Buff, X., Henriksen, C.
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Fractal and Fractional, 2022 In this research, we look at the Julia set patterns that are linked to the entire transcendental function f(z)=aezn+bz+c, where a,b,c∈C and n≥2, using the Mann iterative scheme, and discuss their dynamical behavior.
Darshana J. Prajapati +4 more
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CHECKERBOARD JULIA SETS FOR RATIONAL MAPS [PDF]
International Journal of Bifurcation and Chaos, 2013 In this paper, we consider the family of rational maps [Formula: see text] where n ≥ 2, d ≥ 1, and λ ∈ ℂ. We consider the case where λ 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.
Blanchard, Paul +5 more
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Application of the Fractal Geometry in Development Surya Majapahit Batik Motif
JTAM (Jurnal Teori dan Aplikasi Matematika)The Mandelbrot and Julia sets are generated through iterative mathematical functions applied to points in the complex plane. These operations enable the detailed and intricate patterns characteristic of these fractals, allowing for modifications and ...
Juhari Juhari +1 more
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Constructing non-computable Julia sets [PDF]
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, 2007 We completely characterize the conformal radii of Siegel disks in the family $$P_ (z)=e^{2 i }z+z^2,$$ corresponding to {\bf computable} parameters $ $. As a consequence, we constructively produce quadratic polynomials with {\bf non-computable} Julia sets.
Braverman, Mark, Yampolsky, Michael
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Singular Perturbations of Multibrot Set Polynomials
Universal Journal of Mathematics and Applications, 2022 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.
Figen Çilingir
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