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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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Geometric exponents for hyperbolic Julia sets
TL;DR: In this article, it was shown that the Hausdorff dimension of the Julia set associated to a hyperbolic rational map is bounded away from $2, where the bound depends only on certain intrinsic geometric exponents.
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Dynamics of low-degree rational inner skew-products on $\mathbb{T}^2$
TL;DR: In this article , 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 $\Phi (z_1,z_2) = (\phi (z/1/z/2), z/2)$.
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Frontiers in complex dynamics
TL;DR: In this article, a small constellation of such conjectures centering around the density of hyperbolic rational maps are surveyed, and some of the evidence and logic underlying these conjectures, and sketch recent progress towards their resolution.
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KMS states and branched points
TL;DR: In this paper, the KMS states for the gauge action on a rational function associated with a set of points were completely classified and the degree of the set, the number of branched points, and the orbits of exceptional points.
Random Iteration of Rational Maps
TL;DR: RANDOM ITERATION OF RATIONAL MAPS as mentioned in this paper is an example of such a map-based approach to the problem of RMPs and their application in mapping.