Results 11 to 20 of about 64,522 (306)
Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model [PDF]
Discrete Dynamics in Nature and Society, 2016 Fractal theory is a branch of nonlinear scientific research, and its research object is the irregular geometric form in nature. On account of the complexity of the fractal set, the traditional Euclidean dimension is no longer applicable and the ...
Yuqian Deng +2 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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Quasisymmetrically inequivalent hyperbolic Julia sets
Revista Matemática Iberoamericana, 2012 We give explicit examples of pairs of Julia sets of hyperbolic rational maps which are homeomorphic but not quasisymmetrically homeomorphic.
Haïssinsky, Peter, Pilgrim, Kevin
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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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The Generalized Julia Set Perturbed by Composing Additive and Multiplicative Noises [PDF]
Discrete Dynamics in Nature and Society, 2009 This paper contrastively researches the structural characteristic and the fission-evolution law of four different kinds of generalized Julia set (generalized J set in short) with different parameter c, which includes the generalized J set without any ...
Xingyuan Wang, Ruihong Jia, Yuanyuan Sun
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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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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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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.
Dong Li +3 more
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Julia sets as buried Julia components
Transactions of the American Mathematical Society, 2020 Let f f be a rational map with degree d ≥ 2 d\geq 2 whose Julia set is connected but not equal to the whole Riemann sphere. It is proved that there exists a rational map g g such that g g contains a buried Julia component on which the dynamics is ...
Wang, Youming, Yang, Fei
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Control and synchronization of Julia sets of the complex dissipative standard system
Nonlinear Analysis, 2016 The fractal behaviors of the complex dissipative standard system are discussed in this paper. By using the boundedness of the forward and backward orbits, Julia set of the system is introduced and visualization of Julia set is also given.
Weihua Sun, Yongping Zhang
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