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BookDOI

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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Closure of Periodic Points Over a Non-Archimedean Field

Liang Chung Hsia
- 01 Dec 2000 - 
TL;DR: The closure of the periodic points of rational maps over non-archimedean fields was studied in this paper, where it was shown that the Julia set of a rational map over a non-archemic field is contained in the closure of periodic points.
Journal ArticleDOI

Commutators, collars and the geometry of Möbius groups

Frederick W. Gehring, +1 more
- 01 Dec 1994 - 
Journal ArticleDOI

Local connectivity of the Julia set for geometrically finite rational maps

Lei Tan, +1 more
- 20 Jan 1996 - 
TL;DR: In this paper, it was proved that each (eventually) periodic connected component of the Julia set of a geometrically finite rational map is locally connected, which is the same as proving that each component of a Julia set can be locally connected.
Book

Arithmetic Differential Equations

Alexandru Buium
TL;DR: In this paper, the authors provide an overview of the main concepts and results from algebraic geometry, including preliminary preciminaries of algebraic geometries, and applications of flat correspondences and hyperbolic correspondences.
Journal ArticleDOI

Non-uniform hyperbolicity in complex dynamics

Jacek Graczyk, +1 more
- 01 Feb 2009 - 
TL;DR: In this paper, a rational function F satisfies the summability condition with exponent α if for every critical point c which belongs to the Julia set J there exists a positive integer n ≥ 0.