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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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Spiders' webs and locally connected Julia sets of transcendental entire functions
TL;DR: In this article, it was shown that the Julia set of a transcendental entire function is locally connected and takes the form of a spider's web in the sense defined by Rippon and Stallard.
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Cantor boundary behavior of analytic functions
TL;DR: In this paper, the authors studied the class of analytic functions f(z) for which the image curves of these functions form infinitely many loops everywhere, they are not univalent of course, and they gave sufficient conditions for such property, making use of the distribution of the zeros of f and the mean growth rate of f.
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Study of iterative methods through the Cayley Quadratic Test
TL;DR: This work compares the dynamical behavior on quadratic polynomials with the one of Newton's scheme using what is defined in Cayley Quadratic Test (CQT), which can be used as a first test to check the efficiency of iterative methods for solving nonlinear equations.
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Local uniform convergence and convergence of Julia sets
TL;DR: In this article, the Julia set of S is the whole sphere C for a certain class of entire functions and it is shown that for each singular value c of f there exists a singular value n(n) of fn (for each sufficiently large n) converging to c.
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On pinching deformations of rational maps
TL;DR: In this paper, the authors introduce the notion of the dynamical length of an invariant arc of a rational map R and show that if the sequence converges to a rational mapping, the spherical diameter of the corresponding arc also shrinks to zero.