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Iteration of Rational Functions
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This article is published in American Mathematical Monthly.The article was published on 1991-01-01. It has received 972 citations till now. The article focuses on the topics: Elliptic rational functions & Rational function.read more
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Asymptotic size of Herman rings of the complex standard family by quantitative quasiconformal surgery
TL;DR: In this paper, the complexification of the Arnold standard family of circle maps given by � Fα,e(u) = ue iα e (e/2)(u−1/u), with α = α(e) chosen so that
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Perturbing circle-packing Kleinian groups as correspondences
TL;DR: In this paper, the authors consider perturbations of maximally parabolic representations of a free product C4*C2 of cyclic groups in the wider context of holomorphic correspondences on the Riemann sphere (multivalued maps defined by polynomial relations).
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Entire functions of slow growth whose Julia set coincides with the plane
TL;DR: In this paper, the authors construct a transcendental entire function, which is an arbitrary prescribed function tending to infinity, and construct a set of functions from the entire function and the entire set.
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Some variants of the Chebyshev-Halley family of methods with fifth order of convergence
TL;DR: This paper presents some techniques for constructing high-order iterative methods in order to approximate the zeros of a non-linear equation f(x)=0, starting from a well-known family of cubic iterative processes and analyses the efficiency of these methods.
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Building blocks for quadratic Julia sets
TL;DR: In this article, it was shown that the Julia set of a quadratic polynomial P with an irrationally indifferent fixed point zo in the iterative dynamics of P is not locally connected.