Results 41 to 50 of about 64,522 (306)
Julia sets are uniformly perfect [PDF]
Proceedings of the American Mathematical Society, 1992 We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet. Using this we obtain a formula for the entropy of invariant harmonic measures on Julia sets.
Mañé, R., Da Rocha, L. F.
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Julia and Mandelbrot Sets for Dynamics over the Hyperbolic Numbers
Fractal and Fractional, 2019 Julia and Mandelbrot sets, which characterize bounded orbits in dynamical systems over the complex numbers, are classic examples of fractal sets. We investigate the analogs of these sets for dynamical systems over the hyperbolic numbers.
Vance Blankers +3 more
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Fractal and FractionalThis paper deepens some results on a Mandelbrot set and Julia sets of Caputo’s fractional order. It is shown analytically and computationally that the classical Mandelbrot set of integer order is a particular case of Julia sets of Caputo-like fractional ...
Marius-F. Danca
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Orthogonal Polynomials on Generalized Julia Sets [PDF]
Complex Analysis and Operator Theory, 2017 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. In addition, we discuss optimal smoothness of Green functions and Parreau-Widom criterion for a special family of real generalized Julia sets.
Gökalp Alpan, Alexander Goncharov
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Analysis of Neutrosophic Set, Julia Set in Aircraft Crash
Neutrosophic Sets and SystemsA neutrosophic fuzzy set that generalizes the classical set is represented by a closed interval [0,1]. Let us generalize the fuzzy set to the Neutrosophic set, which is defined as three membership functions between interval ]-0,1+ [.
M.N. Bharathi, G. Jayalalitha
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On the Fractional-Order Complex Cosine Map: Fractal Analysis, Julia Set Control and Synchronization
Mathematics, 2023 In this paper, we introduce a generalized complex discrete fractional-order cosine map. Dynamical analysis of the proposed complex fractional order map is examined. The existence and stability characteristics of the map’s fixed points are explored.
A. A. Elsadany +3 more
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Objectives To identify predictors of chronic ITP (cITP) and to develop a model based on several machine learning (ML) methods to estimate the individual risk of chronicity at the timepoint of diagnosis. Methods We analyzed a longitudinal cohort of 944 children enrolled in the Intercontinental Cooperative immune thrombocytopenia (ITP) Study ...
Severin Kasser +6 more
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Julia sets and differential equations [PDF]
Proceedings of the American Mathematical Society, 1993 Summary: A one-parameter family of Julia sets is shown to converge, in a probabilistic sense, to certain trajectories of a differential equation. The Julia sets arise from Euler's method for the differential equation. This provides information on the location of the Julia sets and the dynamics on them.
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International Journal of Mathematics and Mathematical Sciences, 2001 In 1977 Hubbard developed the ideas of Cayley (1879) and solved in particular the Newton-Fourier imaginary problem. We solve the Newton-Fourier and the Chebyshev-Fourier imaginary problems completely.
Anna Tomova
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Fractal and Fractional, 2021 In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of ...
Yang Zhao +3 more
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