Results 31 to 40 of about 263,389 (315)
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.
Peter Haı̈ssinsky, Kevin M. Pilgrim
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Semi-hyperbolic fibered rational maps and rational semigroups [PDF]
, 2006 We consider fiber-preserving complex dynamics on fiber bundles whose fibers are Riemann spheres and whose base spaces are compact metric spaces. In this context, without any assumption on (semi-)hyperbolicity, we show that the fiberwise Julia sets are ...
Sumi, Hiroki
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Visualization of Mandelbrot and Julia Sets of Möbius Transformations
Fractal and Fractional, 2021 This work reports on a study of the Mandelbrot set and Julia set for a generalization of the well-explored function η(z)=z2+λ. The generalization consists of composing with a fixed Möbius transformation at each iteration step.
Leah K. Mork, Darin J. Ulness
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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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Julia Sets in Parameter Spaces [PDF]
Communications in Mathematical Physics, 2001 The paper is devoted to study the one parameter family of cubic polynomials \[ g_b(z)= \lambda z+ bz^2+z^3, \quad b\in \mathbb{C},\tag{1} \] where \(\lambda= e^{2\pi i\theta}\) is a fixed complex number of modulus 1. The authors show that the bifurcation locus of (1) contains quasi-conformal copies of the quadratic Julia set \(J(\lambda z+z^2)\).
Buff, X., Henriksen, C.
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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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On the dynamics of a family of renormalization transformations [PDF]
, 2013 We study the family of renormalization transformations of the generalized $d$--dimensional diamond hierarchical Potts model in statistical mechanic and prove that their Julia sets and non-escaping loci are always connected, where $d\geq 2$. In particular,
Yang, Fei, Zeng, Jinsong
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Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
Discrete Dynamics in Nature and Society, 2020 The fractional Potts model on diamond-like hierarchical lattices is introduced in this manuscript, which is a fractional rational system in the complex plane. Then, the fractal dynamics of this model is discussed from the fractal viewpoint.
Weihua Sun, Shutang Liu
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Constructing non-computable Julia sets [PDF]
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, 2007 We completely characterize the conformal radii of Siegel disks in the family $$P_ (z)=e^{2 i }z+z^2,$$ corresponding to {\bf computable} parameters $ $. As a consequence, we constructively produce quadratic polynomials with {\bf non-computable} Julia sets.
Braverman, Mark, Yampolsky, Michael
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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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