Results 11 to 20 of about 1,964,264 (277)
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.
Mañé, R., Da Rocha, L. F.
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The omega-limit sets of quadratic Julia sets
, 2012 In this paper we characterize $\w$-limit sets of dendritic Julia sets for quadratic maps. We use Baldwin's symbolic representation of these spaces as a non-Hausdorff itinerary space and prove that quadratic maps with dendritic Julia sets have shadowing, and also that for all such maps, a closed invariant set is an $\w$-limit set of a point if, and only
Barwell, Andrew D., Raines, Brian E.
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Consensus of Julia Sets of Potts Models on Diamond-Like Hierarchical Lattice
IEEE Access, 2022 The limit sets of zeros of the partition function for $\lambda $ -state Potts models on diamond-like hierarchical lattice are the Julia sets of functions in a family of rational functions. In this paper, the consensus problem of Julia sets generated by
Xiaoling Lu, Weihua Sun
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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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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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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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Julia Sets of Orthogonal Polynomials [PDF]
Potential Analysis, 2018 14 pages, 1 ...
Jacob Stordal Christiansen +3 more
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Quasisymmetries of finitely ramified Julia sets. [PDF]
Math AnnWe develop a theory of quasisymmetries for finitely ramified fractals, with applications to finitely ramified Julia sets. We prove that certain finitely ramified fractals admit a naturally defined class of “undistorted metrics” that are all ...
Belk J, Forrest B.
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Julia sets and wild Cantor sets [PDF]
Geometriae Dedicata, 2014 There exist uniformly quasiregular maps $f:\mathbb{R}^3 \to \mathbb{R}^3$ whose Julia sets are wild Cantor sets.
Fletcher, Alastair, Wu, Jang-Mei
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