BookDOI
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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Equicontinuous Actions on Semi-Locally Connected and Local Dendrites
TL;DR: In this paper, a necessary and sufficient condition for equicontinuous semi-locally connected flow with almost automorphic points is given, which is a generalization of Morales's results.
Journal ArticleDOI
Infinite basins of julia sets
TL;DR: The goal of this paper is to investigate the iterative behavior of a particular class of rational functions which arise from Newton's method applied to the entire function (z2 + c)eQ(z) where c is a complex parameter and Q is a nonconstant polynomial with deg(Q) ≤ 2.
Book ChapterDOI
Elliptic Functions: An application of elliptic functions in algebra – solution of the general quintic equation
J. V. Armitage,W. F. Eberlein +1 more
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Green functions on self-similar graphs and bounds for the spectrum of the Laplacian
TL;DR: In this paper, a graph theoretic analogue to the Banach fixed point theorem is proved for self-similar graphs, which correspond to general nested but not necessarily finitely ramified fractals, by combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis.
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Hereditarily non Uniformly Perfect analytic and conformal non-autonomous attractor sets
TL;DR: In this article, conditions are given which imply that certain non-autonomous analytic iterated function systems in the complex plane have pointwise thin, and thus hereditarily non uniformly perfect, attractor sets.