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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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Dynamics of low-degree rational inner skew-products on $\mathbb{T}^2$
Alan Sola,Ryan Tully-Doyle +1 more
TL;DR: In this paper, the authors examine iteration of certain skew-products on the bidisk whose components are rational inner functions, with emphasis on simple maps of the form (πi(z_1,z_2) = (π(π(z/1,π/2), z/2) ).
Journal ArticleDOI
Geometric limit of Julia set of a family of rational functions with odd degree
TL;DR: For a positive odd integer d, the authors studied the connectedness of the Julia set of the one-parameter family of rational maps given by Rc(z) = c(zd−(d−1))/z with c∈R∖{0}.
Holomorphic Dynamics and Hyperbolic Geometry
TL;DR: In this article, the authors introduce the main techniques and results in the two areas, emphasising the strong connections and parallels between them, and introduce some of the main results and techniques.
Proceedings ArticleDOI
Stability Problems in Symbolic Integration
TL;DR: In this paper , a dynamical aspect of symbolic integration by studying stability problems in differential fields is proposed, and three special families of stable elementary functions including rational functions, logarithmic functions, and exponential functions are characterized.
Journal ArticleDOI
Continuity of filled-in Julia sets and the closing lemma
TL;DR: In this paper, the continuity of filled-in Julia sets of functions meromorphic in the complex plane has been studied and a closed lemma for polynomials and entire transcendental functions is proven.