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
Citations
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Singular perturbations of complex polynomials and circle inversion maps
Daniel M. Look,Robert L. Devaney +1 more
TL;DR: In this paper, the dynamics of the family of complex functions Flz =z n+l/zd is explored and a complete description of the symbolic dynamics of Fl restricted to its Julia set (in the cases where the Julia set is a Sierpinski curve) is given.
Journal ArticleDOI
On the Simple Connectivity of Fatou Components
Chunlei Cao,Yuefei Wang +1 more
TL;DR: In this article, it was shown that for certain holomorphic maps, all Fatou components are simply connected, and the relation between wandering domains and singularities for certain meromorphic maps was discussed.
Dissertation
Measurable dynamics of meromorphic maps
TL;DR: In this paper, the authors studied how the orbits of the singularities of the inverse of a meromorphic function prescribe the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero.
Journal ArticleDOI
Long-term orbit dynamics viewed through the yellow main component in the parameter space of a family of optimal fourth-order multiple-root finders
Young Hee Geum,Young Ik Kim +1 more
TL;DR: In this paper, an analysis based on an elementary theory of plane curves is presented to locate bifurcation points from a main component in the parameter space of a family of optimal fourth-order multiple-root finders.
Journal ArticleDOI
Negativity of Lyapunov Exponents and Convergence of Generic Random Polynomial Dynamical Systems and Random Relaxed Newton’s Methods
TL;DR: In this paper, the authors studied random complex dynamical systems generated by probability measures on finite unions of the loci of holomorphic families of rational maps on the Riemann sphere.