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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Entropy of Irregular Points for Some Dynamical Systems
TL;DR: In this article , sufficient conditions for a dynamical system to have a set of irregular points with full topological entropy were derived and verified for nonuniformly hyperbolic systems such as positive entropy surface diffeomorphisms and rational functions on the Riemann sphere.
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On buried points and phase transition points in the Julia sets concerning renormalization transformation
TL;DR: In this paper, a family of rational maps concerning renormalization transformation is considered and a description of buried points and phase transition points in the Julia set is given, where all points are buried points for some parameters n and λ, according to the problem that Curry and Mayer proposed.
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Singular Perturbations of Multibrot Set Polynomials
TL;DR: In this paper , the authors give a complete description of the dynamics of rational maps arising from Newton's method, where the polynomial of Newton's iteration function is obtained from singularly perturbed versions of the Multibrot set polynomials.
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Eigenvalues in Filled Julia Sets
TL;DR: In this paper, the authors show how Julia sets can be introduced very naturally in a junior-level linear algebra course, as a way of exposing students to the contemporary area of complex dynamics.