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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, Liu Shutang
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Boundaries of Filled Julia Sets in Generalized Jungck Mann Orbit
IEEE Access, 2019 In this paper, we study the generalized Jungck Mann orbit (GJMO) and prove the converse theorem of results. We develop algorithms for the generation of filled Julia sets and their boundaries in the GJMO.
Muhammad Tanveer, Waqas Nazeer
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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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ALTERNATED JULIA SETS AND CONNECTIVITY PROPERTIES [PDF]
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2009 In this work we present the alternated Julia sets, obtained by alternated iteration of two maps of the quadratic family [Formula: see text] and prove analytically and computationally that these sets can be connected, disconnected or totally disconnected verifying the known Fatou–Julia theorem in the case of polynomials of degree greater than two. Some
Marius-F Danca
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Ukrainian Mathematical Journal, 2022 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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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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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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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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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 of Orthogonal Polynomials [PDF]
Potential Analysis, 2018 14 pages, 1 ...
Jacob Stordal Christiansen +3 more
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