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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An optimal eighth-order class of three-step weighted Newton's methods and their dynamics behind the purely imaginary extraneous fixed points
TL;DR: An optimal class of three-step eighth-order methods with higher order weight functions employed in the second and third sub-steps is developed along with a main theorem stating the order of convergence and the asymptotic error constant.
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Semiconjugacies between the Julia sets of geometrically finite rational maps
TL;DR: In this article, a rational map f is called geometrically finite if every critical point contained in its Julia set is eventually periodic and if a perturbation of f into another rational map is horocyclic and preserves the critical orbit relations with respect to the Julia set of f, then a semiconjugacy or a topological conjugacy between their dynamics on the Julia sets is constructed.
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Jordan domain and Fatou set concerning diamond-like hierarchical Potts models
TL;DR: For the Potts models on the diamond-like hierarchical lattice, the domains of the complex phases are indeed the Fatou components of a family of rational maps as discussed by the authors, and the relationships between this family of fatou components and the Jordan domains are described completely.
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Wandering domains and nontrivial reduction in non-archimedean dynamics
TL;DR: In this article, it was shown that the Fatou set of rational functions has wandering components and that the existence of a wandering domain implies that some iterate has nontrivial reduction in some coordinate.
Journal ArticleDOI
On the dynamics of a family of singularly perturbed rational maps
Jianxun Fu,Fei Yang +1 more
TL;DR: In this paper, the authors studied the dynamical behavior of the family of complex rational maps, which can be seen as a perturbation of the unicritical polynomial z ↦ z n if λ is small.