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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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Julia Sets of Joukowski-Exponential Maps
TL;DR: In this paper, a detailed study of the Julia sets of Joukowski-exponential maps is undertaken when it is not equal to the whole sphere, and the Julia set contains two topologically as well as dynamically distinct completely invariant subsets.
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Complex asymptotics of Poincar\'e functions and properties of Julia sets
TL;DR: In this paper, the asymptotic behavior of the solutions of Poincar\'e's functional equation is studied in angular regions of the complex plain and inequalities for multipliers of Pommerenke-Levin-Yoccoz type are given for real Julia sets.
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An Overview of Complex Fractal Dimensions: From Fractal Strings to Fractal Drums, and Back
TL;DR: The theory of complex fractal dimensions and their associated geometric or fractal zeta functions is discussed in this article. But the main goal of this article is to provide an overview of the theory of these dimensions.
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Bers embedding of the teichmÜller space of a once-punctured torus
Yohei Komori,Toshiyuki Sugawa +1 more
TL;DR: In this article, a method of computing monodromies of projective structures on a once-punctured torus is presented, which leads to an algorithm numerically visualizing the shape of the Bers embedding of a one-dimensional Teichmüller space.
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Isospectral deformations of the Dirac operator
TL;DR: In this paper, an integrable system in which the Dirac operator D =d+d^* on a finite simple graph G or Riemannian manifold M is deformed using a Hamiltonian system D'=[B,h(D)] with B=d-d^*) + i b.