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
Citations
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Journal ArticleDOI
Frequency-Dependent Selection in a Periodic Environment.
Robert Forster,Claus O. Wilke +1 more
TL;DR: This work examines the action of natural selection in a periodically changing environment where two competing strains are specialists respectively for each environmental state and shows that coexistence rather than extinction is the likely outcome.
Dissertation
Fields with the Bogomolov property
TL;DR: In this paper, the authors studied the Bogomolov property relative to rational functions in the dynamical setting and proved that the maximal totally real field has the BogOMOLOV property for rational functions over algebraic numbers.
Book ChapterDOI
Chapter 8 Advanced Topics in the Theory of Functions
Umberto Bottazzini,Jeremy Gray +1 more
TL;DR: In this article, the authors look at how the ideas of the founders led to important developments in the theory of complex functions itself and discover some of the central features of complex function theory as a rich research topic in its own right.
Journal ArticleDOI
Hausdorff dimension of quadratic rational Julia sets
Jia Zhou,Liang Wen Liao +1 more
TL;DR: In this paper, the Julia set of a quadratic rational map with a Siegel disk and a fixed point is shown to have a Hausdorff dimension strictly less than two.
Existence of the Mandelbrot Set in the Parameter Planes of Certain Rational Functions
TL;DR: Mitchell et al. as discussed by the authors studied rational functions of the form Rn,a,c(z) = z n + a zn + c and their critical orbits and showed that homeomorphic copies of the Mandelbrot set exist in both the a and c-parameter planes.