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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On the classification of laminations associated to quadratic polynomials
TL;DR: In this paper, it was shown that the topology of such laminations determines the combinatorics of the parameter, i.e., it determines whether a lamination is associated with a periodic critical point.
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McMullen’s root-finding algorithm for cubic polynomials
TL;DR: In this article, it was shown that a generally convergent root-finding algorithm for cubic polynomials defined by C. McMullen is of order 3, and that general convergent algorithms of order 5 and higher are known.
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On the Zeros of Solutions of Linear Differential Equations of the Second Order
TL;DR: In this article, it was shown that the iterates of f converge on an open dense subset of the plane if they converge for the zeros of R. This result is based on the iteration theory of meromorphic functions and in particular on the result that if the family of K-quasiconformal deformations of a meromorphic function f depends on only finitely many parameters, then every cycle of Baker domains of f contains a singularity of f−1.
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COMPLEX DYNAMICS AND INVARIANT FORMS MOD p
TL;DR: In this paper, the authors characterize the dynamical systems that possess invariant forms for all but finitely many places on the Riemann sphere, and present a list of such systems.
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On the Dynamics of the Rational Family $f_{t}(z)=- t/4{(z^{2}- 2)^{2}/(z^{2}- 1)}$
Hye Gyong Jang,Norbert Steinmetz +1 more
TL;DR: In this paper, the authors discuss the dynamics as well as the structure of the parameter space of the one-parameter family of rational maps and show that for any escape parameter t, the boundary of the basin at infinity A t is either a Cantor set, a curve with infinitely many complementary components, or else a Jordan curve.