منابع مشابه
Julia Sets Are Uniformly Perfect
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 loganthmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dinchlet. Using this we obtain a formula for the entropy of invanant harmonic measures on Julia sets. As a corollary we give a very short proof of ...
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The iterates of a uniformly quasiregular map acting on a Riemannian manifold are quasiregular with a uniform bound on the dilatation. There is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We construct the first examples of uniformly quasiregular mappings that have a 2-torus as the Julia set. The spaces supporting this type of mappings incl...
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Using computer graphics and visualization algorithms, we extend in this work the results obtained analytically in [1], on the connectivity domains of alternated Julia sets, defined by switching the dynamics of two quadratic Julia sets. As proved in [1], the alternated Julia sets exhibit, as for polynomials of degree greater than two, the disconnectivity property in addition to the known dichoto...
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Very often in analysis, one focuses on connected spaces. This is certainly not always the case, and in particular there are many interesting matters related to Cantor sets. Here we are more concerned with a type of complementary situation. As a basic scenario, suppose that U is an open set in Rn and that E is a closed set contained in the boundary of U such that for every x ∈ U and r > 0 there ...
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Abstract: Motivated by Lévy’s characterization of Brownian motion on the line, we propose an analogue of Brownian motion that has as its state space an arbitrary closed subset of the line that is unbounded above and below: such a process will be a martingale, will have the identity function as its quadratic variation process, and will be “continuous” in the sense that its sample paths don’t ski...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2021
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-021-02699-6