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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Attractors in quasiregular semigroups
Aimo Hinkkanen,Gaven Martin +1 more
TL;DR: In this article, it was shown that the attracting and repelling fixed points of elements of uniformly quasimeromorphic semigroups such that the element is locally homeomorphic at the fixed point are quasiconformally conjugate to a dilation in a neighbourhood of such a point.
Journal ArticleDOI
Singular Perturbations of Quadratic Maps
TL;DR: Two generalizations are considered: the case of complex e and the mapping z→zn+(e/zm), where e is positive and real, and a full characterization of the map for a certain set of parameters.
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Orthogonal and L q -extremal polynomials on inverse images of polynomial mappings
TL;DR: In this paper, it was shown that the minimum deviation of polynomials orthogonal with respect to a positive measure on T − 1 (∂K) behaves asymptotically periodic and that the orthogonality of the polynomial polynomorphs on Julia sets has an asyptotic behaviour.
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Area of Fatou sets of trigonometric functions
TL;DR: In this paper, it was shown that the area of the Fatou set of the sine function in a vertical strip of width 2π is finite, which confirms a conjecture by Milnor.
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Partition function zeros of the one-dimensional Potts model: The recursive method
TL;DR: In this paper, Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model were studied using the theory of dynamical systems and an exact recurrence relation for the partition function was derived.