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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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Geometric Limits of Julia Sets of Maps z n + exp(2πiθ) as n → ∞
TL;DR: It is shown that the geometric limit as n → ∞ of the Julia sets J(Pn, c) for the maps Pn,c(z) = zn + c does not exist for almost every c on the unit circle.
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Topological transitivity and chaos of group actions on dendrites
TL;DR: It is shown that each weakly mixing group action on a dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated.
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Slices of Parameter Space for Meromorphic Maps with Two Asymptotic Values
TL;DR: In this article, the authors give a full description of the parameter space for a specific family based on the exponential function that has precisely two finite asymptotic values and one attracting fixed point.
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Classifying simply connected wandering domains
TL;DR: In this article, a detailed classification of the dynamics in simply connected wandering domains in terms of the hyperbolic distances between iterates and also the behaviour of orbits in relation to the boundaries of the wandering domains is given.