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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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Exploration of Filled-In Julia Sets Arising from Centered Polygonal Lacunary Functions [PDF]
Fractal and Fractional, 2019 Centered polygonal lacunary functions are a particular type of lacunary function that exhibit properties which set them apart from other lacunary functions. Primarily, centered polygonal lacunary functions have true rotational symmetry.
L.K. Mork +4 more
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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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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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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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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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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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AIMS Mathematics, 2023 In the value distribution theory of complex analysis, Petrenko's deviation is to describe more precisely the quantitative relationship between $ T (r, f) $ and $ \log M (r, f) $ when the modulus of variable $ |z| = r $ is sufficiently large.
Guowei Zhang
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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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A New Measure of Quantum Starlike Functions Connected with Julia Functions
Journal of Function Spaces, 2022 In a complex domain, the investigation of the quantum differential subordinations for starlike functions is newly considered by few research studies. In this note, we arrange a set of necessary conditions utilizing the concept of the quantum differential
Samir B. Hadid +2 more
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