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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Continuity and hausdorff dimension of julia set concerning yang-lee zeros
Gao Junyang,Qiao Jianyong +1 more
TL;DR: Considering the Julia set J(Tλ) of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, this paper proved that JTλ > 1 and discussed the continuity of JTl in Hausdorff topology for λ ∈ R.
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Dynamical analysis to explain the numerical anomalies in the family of ermakov-kalitlin type methods
TL;DR: A complex dynamical analysis of the dynamics of an iterative method based on the Ermakov-Kalitkin class of iterative schemes for solving nonlinear equations is made in order to justify the stability properties of this family.
Journal ArticleDOI
On quasi-discs and Fatou components of a family of rational maps concerning renormalization transformation
TL;DR: In this article, the relation between quasi-discs and the Fatou components of Tnλ is studied and the boundary of each Fatou component is a quasi-circle or not for parameters n ∈ N and λ ∈ R.
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The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function
Christian Berg,Antonio J. Durán +1 more
TL;DR: In this paper, the fixed point for a non-linear transformation in the set of Hausdorff moment sequences was studied, defined by the formula: T((a_n))_n=1/(a_0+... +a_ n) ).
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Exponential growth of some iterated monodromy groups
Mikhail Hlushchanka,Daniel Meyer +1 more
TL;DR: In this article, the authors show exponential growth of several non-polynomial rational maps, such as rational maps whose Julia set is the whole sphere, rational maps with Sierpinski carpet Julia set, and obstructed Thurston maps, and construct the first example of a non-renormalizable polynomial with a dendrite Julia set with exponential growth.