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Fractal and Fractional, 2022 The Julia set is one of the most important sets in fractal theory. The previous studies on Julia sets mainly focused on the properties and graph of a single Julia set.
Weihua Sun, Shutang Liu
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On escape criterion of an orbit with s-convexity and illustrations of the behavior shifts in Mandelbrot and Julia set fractals. [PDF]
PLoS ONEOur study presents a novel orbit with s-convexity, for illustration of the behavior shift in the fractals. We provide a theorem to demonstrate the escape criterion for transcendental cosine functions of the type Tα,β(u) = cos(um)+αu + β, for [Formula ...
Khairul Habib Alam +4 more
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Computability of Julia Sets [PDF]
Moscow Mathematical Journal, 2008 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. We also show that a filled Julia set of a polynomial is always computable.
Braverman, Mark, Yampolsky, Michael
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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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Complex Dynamics of the family [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2010 The aim of this work is to study the complex dynamics of the family F={ ,}, of transcendental meromorphic functions. We prove that certain intervals are contained in J(f) or in F(f ) and we prove that Julia set contains and show that Fatou set of the ...
Salma Faris
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Synchronization of Julia Sets in Three-Dimensional Discrete Financial Models
Fractal and Fractional, 2023 When aiming to achieve consistency in fractal characteristics between different models, it is crucial to consider the synchronization of Julia sets.
Zhongyuan Zhao +2 more
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Exploring parameter spaces in complex dynamics
Selecciones Matemáticas, 2023 We show the structure of the parameter space for a family of rational maps containing Blaschke products. Through numerical simulations using the orbit of a single critical point, we reveal the existence of infinitely many Mandelbrot-like sets along the ...
Pedro Iván Suárez Navarro
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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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The Hausdorff dimension of the Julia sets concerning generated renormalization transformation
AIMS Mathematics, 2022 Considering a family of rational map $ {U_{mn\lambda }} $ of the renormalization transformation of the generalized diamond hierarchical Potts model, we give the asymptotic formula of the Hausdorff dimension of the Julia sets of $ {U_{mn\lambda }} $ as ...
Tingting Li, Junyang Gao
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