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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Generalized Mandelbrot sets for meromorphic complex and quaternionic maps
TL;DR: Three-dimensional sections of the Cycle sets of QRM are nontrivial extensions of the cycle sets of complex maps, while sharing many of their features of the Mandelbrot set.
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Residual Julia Sets of Meromorphic Functions
TL;DR: In this article, the residual Julia sets of meromorphic functions are studied and it is shown that if a meromorphic function f belongs to the class S and its Julia set is locally connected, then the residual residual Julia set of f is empty if and only if its Fatou set F(f) has a completely invariant component or consists of only two components.
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Meromorphic multifunctions in complex dynamics
L. Baribeau,T. J. Ransford +1 more
TL;DR: In this article, it was shown that the upper semicontinuous regularization of the Julia set of R λ is a meromorphic multifunction, and that it is possible to obtain a Julia set that coincides with j (λ) for all λ in a dense open set.
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Symmetries of the Julia sets of Newton’s method for multiple root
TL;DR: It is shown that the group of symmetries of Julia set of polynomial is a subgroup of that of the corresponding standard, multiple and relax Newton’s method when a nonlinear polynometric is in normal form and the Julia set has finite group of symmetry.
Journal ArticleDOI
Geometric limits of Mandelbrot and Julia sets under degree growth
TL;DR: For the family Pn,c(z) = zn + c, the authors showed that the geometric limit of the Mandelbrot sets Mn(P) as n → ∞ exists and is the closed unit disk.