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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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Functions with No Unbounded Fatou Components.
TL;DR: For a transcendental entire function, a partial affirmative answer to Baker's question on the boundedness of its Fatou components is given in this paper, and Wang's answer on Fejer gaps is given.
Journal ArticleDOI
Note on infinitely connected immediate basins of attracting cycles for iteration of rational functions
TL;DR: In this paper, the authors give examples of rational functions, each of whose Fatou sets contains an immediate basin of a super-attracting cycle of period 2 which is infinitely connected.
Journal ArticleDOI
Uniformly perfect Julia sets of meromorphic functions
Sheng Wang,Liang-Wen Liao +1 more
TL;DR: In particular, Julia sets of meromorphic functions are uniformly perfect under some suitable conditions as discussed by the authors, and so are Julia sets associated with a finitely generated semigroup of rational functions.
Properties of the Julia Set of a Rational Map
TL;DR: The theory of iteration of rational maps is a relatively new area in mathematics, which has enjoyed a bit of a renaissance the last three decades thanks to computer images that reveal the beauty of the Mandelbrot set and various Julia sets.