BookDOI
Iteration of Rational Functions
About:
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
More filters
Journal ArticleDOI
Random complex dynamics and devil's coliseums
TL;DR: In this paper, the authors studied the dynamics of a semigroup of polynomials whose planar postcritical set is bounded and the associated random dynamics are studied, and they showed that the Julia set of such a semiigroup may be disconnected.
Posted Content
The dynamics of semigroups of transcendental entire functions II
Dinesh Kumar,Sanjay Kumar +1 more
TL;DR: In this paper, the concept of escaping set for semigroups of transcendental entire functions using Fatou-Julia theory was introduced, and several results of the escaping set associated with the iteration of one transversal entire function have been extended to transcendental semigroup.
Journal ArticleDOI
Proof of a dynamical bogomolov conjecture for lines under polynomial actions
Dragos Ghioca,Thomas J. Tucker +1 more
TL;DR: In this article, a dynamical version of the Bogomolov conjecture was proved for lines in A m under the action of a map (f1,:::;fm) where each fi is a polynomial in Q(X) of the same degree.
Journal ArticleDOI
A Note on the Maximum Number of Zeros of $r(z) - \bar{z}$
TL;DR: In this paper, it was shown that the complex harmonic function of the form r(z) - \bar{z} has at most 5 (n − 1) zeros.
Journal ArticleDOI
Rational maps whose Julia sets are Cantor circles
TL;DR: In this paper, the authors give a family of rational maps whose Julia sets are Cantor circles and show that every rational map whose Julia set is a Cantor set of circles must be topologically conjugate to one map in this family on their corresponding Julia sets.