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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Book ChapterDOI
Elliptic Curves over $$\mathbb{C}$$
TL;DR: In this paper, the arc length of an ellipse was shown to be not computable in terms of so-called elementary functions, and an inverse trigonometric function was derived.
Posted Content
Singular perturbations of Blaschke Products and connectivity of Fatou components
TL;DR: In this article, the authors studied the singular perturbations of Blaschke products and proved that the Julia set is the union of countably many Cantor sets of quasicircles and uncountably many point components.
Posted Content
Singular perturbations with multiple poles of the simple polynomials
Yingqing Xiao,Fei Yang +1 more
TL;DR: In this paper, the dynamics of the Julia sets of rational maps with one parameter were studied and a characterization of the topological properties of Julia sets was given according to the dynamical behaviors of the orbits of the free critical points.
Rational maps lacking certain periodic orbits
TL;DR: In this article, the dynamics of rational maps without certain periodic points, focusing on the roles of critical points, are studied. But the authors do not consider the case where critical points do not have periodic points.
Journal ArticleDOI
{\L}S condition for filled Julia sets in $\mathbb{C}$
TL;DR: In this article, an inequality of Łojasiewicz-Siciak type for certain sets arising in the context of complex dynamics in dimension 1 was derived, which highlights an interesting class of compact sets satisfying this condition.