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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A Note on the Maximum Number of Zeros of $$r(z) - \overline{z}$$
TL;DR: In this paper, it was shown that the complex harmonic function of the form R(z) - \overline{z} has at most 5 (n − 1) zeros.
Journal ArticleDOI
On a Family of Rational Perturbations of the Doubling Map
TL;DR: In this paper, the authors investigate the parameter plane of a rational family of perturbations of the doubling map given by the Blaschke products and explore the relation between certain members of the family and the degree 4 polynomials.
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Cooperation principle, stability and bifurcation in random complex dynamics
TL;DR: In this paper, the authors investigated random complex dynamics of rational or polynomial maps on the Riemann sphere, and they showed that the chaos of the averaged system disappears at any point in the system, due to the automatic co-opeartion of many kinds of maps.
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Embeddings of trees in the hyperbolic disk
Joel M. Cohen,Flavia Colonna +1 more
TL;DR: In this paper, the authors consider the conditions under which a homogeneous tree of even degree (i.e. the Cayley graph of a free group) may be embedded in the hyperbolic disk in such a way that the automorphisms induced by rotation and by translation by group elements may be represented by automomorphisms of the disk.
Journal ArticleDOI
Partition function zeros of the one-dimensional Potts model: the recursive method
TL;DR: In this article, the Yang-Lee, Fisher and Potts zeros of the one-dimensional Q-state Potts model are studied using the theory of dynamical systems and an exact recurrence relation for the partition function is derived.