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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Journal ArticleDOI
Meromorphic functions of the form $f(z) = \sum_{n=1}^\infty a_n/(z - z_n)$
James K. Langley,John Rossi +1 more
TL;DR: In this paper, the authors prove some results on the zeros of functions of the form f(z) = Sn = 18 an/(z - zn) using quasiconformal surgery, Fourier series methods, and Baernstein's spread theorem.
Journal ArticleDOI
Complex dynamics of Möbius semigroups
TL;DR: In this article, Caruso's family of Mobius semigroups, based on a random dynamics variant of the Fibonacci sequence, is studied and compared to rational functions, rational semiggroups, and Mobius groups.
Journal ArticleDOI
On functions of bounded type
TL;DR: In this paper, the authors consider certain functions meromorphic in the plane that are of bounded type in suitable half planes and deduce that conditions of being positive semi-definite on matrices whose elements depend on a function f, determine f uniquely.
Dissertation
Integral transforms of the Minkowski question mark function
TL;DR: The Minkowski question mark function F(x) arises as a real distribution function of rationals in the Farey (alias, Stern-Brocot or Calkin-Wilf) tree.
Journal ArticleDOI
Laplace Operators on Fractals and Related Functional Equations
TL;DR: In this paper, the authors give an overview over the application of functional equations, namely the classical Poincare and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals.