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Iteration of Rational Functions

Robert L. Devaney, +1 more
- 01 Jan 1991 - 
- Vol. 100, Iss: 1, pp 90
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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.

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Geometric construction and analytic representation of Julia sets of polynomial maps

Ovidiu Costin, +1 more
- 01 Apr 2011 - 
TL;DR: In this paper, it was shown that the Julia set of a quadratic map is given by transseries formulae, rapidly convergent as repelling periodic points are approached.
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Roots of two‐terminal reliability polynomials

Jason I. Brown, +1 more
- 01 Sep 2021 - 
Journal ArticleDOI

A Julia Set That Is Everything

Julia Barnes, +1 more
- 01 Oct 2003 - 
TL;DR: In this article, it was shown that for polynomials, there must always be some large region where the function has very predictable behavior, and the picture of such an example would be entirely black, and even the casual reader will observe from pictures that all of these Julia sets appear to have area zero.
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Accessible Boundary Points in the Shift Locus of a Familiy of Meromorphic Functions with Two Finite Asymptotic Values

Tao Chen, +2 more
- 30 Jan 2020 - 
TL;DR: In this article, the bifurcation locus of a family of meromorphic functions with two asymptotic values, no critical values, and an attracting fixed point was studied.
Journal ArticleDOI

Newly reducible iterates in families of quadratic polynomials

Katharine Chamberlin, +5 more
- 31 Dec 2012 - 
TL;DR: For fixed n 3 and nearly all values of, the authors showed that there are only finitely many m such that g; m has a newly reducible n-th iterate.