Results 11 to 20 of about 263,389 (315)
Computability of Julia sets [PDF]
Moscow Mathematical Journal, 2007 In this paper we settle most of the open questions on algorithmic computability of Julia sets. In particular, we present an algorithm for constructing quadratics whose Julia sets are uncomputable.
Braverman, Mark, Yampolsky, Michael
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Orthogonal polynomials on generalized Julia sets [PDF]
Complex Analysis and Operator Theory, 2016 We extend results by Barnsley et al. about orthogonal polynomials on Julia sets to the case of generalized Julia sets. The equilibrium measure is considered.
Alpan, Gökalp, Goncharov, Alexander
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Shapes of Polynomial Julia Sets [PDF]
Ergodic Theory and Dynamical Systems, 2013 Any Jordan curve in the complex plane can be approximated arbitrarily well in the Hausdorff topology by Julia sets of polynomials. Finite collections of disjoint Jordan domains can be approximated by the basins of attraction of rational maps.Comment: 13 ...
Hubbard, KATHRYN A. LINDSEY, Sullivan
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Checkerboard Julia Sets for Rational Maps [PDF]
International Journal of Bifurcation and Chaos, 2011 In this paper, we consider the family of rational maps $$\F(z) = z^n + \frac{\la}{z^d},$$ where $n \geq 2$, $d\geq 1$, and$\la \in \bbC$. We consider the case where $\la$ lies in the main cardioid of one of the $n-1$ principal Mandelbrot sets in these ...
Blanchard, Paul +5 more
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Disconnected Julia set and rotation sets [PDF]
Annales scientifiques de l'École normale supérieure, 1996 Let \(f_c(z) = z^2+c\), and \(M= \{c\in \mathbb{C}:f^n_c(0)\) bounded for \(n\in\mathbb{N}\}\) the Mandelbrot set. Let \(\Psi\) be the conformal map from the complement of the unit disc \(D\) to the complement of \(M\), such that \(\Psi(w) \sim w\) as \(w\to\infty\). The boundary behaviour of this map is of the greatest interest.
Genadi Levin
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Ukrainian Mathematical Journal, 2021 UDC 517.5 For a familiy of holomorphic functions on an arbitrary domain, we introduce Fatou and Julia like sets, and establish some of their interesting properties.
Charak, K. S., Singh, A., Kumar, M.
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Julia sets and wild Cantor sets [PDF]
Geometriae Dedicata, 2014 There exist uniformly quasiregular maps $f:\mathbb{R}^3 \to \mathbb{R}^3$ whose Julia sets are wild Cantor sets.
Fletcher, Alastair, Wu, Jang-Mei
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Julia Sets of Orthogonal Polynomials [PDF]
Potential Analysis, 2018 14 pages, 1 ...
Jacob Stordal Christiansen +3 more
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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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A Four Step Feedback Iteration and Its Applications in Fractals
Fractal and Fractional, 2022 Fractals play a vital role in modeling the natural environment. The present aim is to investigate the escape criterion to generate specific fractals such as Julia sets, Mandelbrot sets and Multi-corns via F-iteration using complex functions h(z)=zn+c, h ...
Asifa Tassaddiq +4 more
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