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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Dynamics of infinitely generated nicely expanding rational semigroups and the inducing method
TL;DR: In this article, a fractal theory of the Julia sets of infinitely generated semigroups of rational maps was established, and a new class of semigroup which is called nicely expanding rational semiigroups was introduced, and Bowen's formula for the Hausdorff dimension of the pre-Julia sets was proved.
Estimates of linearization discs in p-adic dynamics with application to ergodicity
TL;DR: In this paper, Lindahl et al. gave lower bounds for the size of linearization disc for power series over quadratic maps, and certain power series containing a sufficiently large quadrastic term, and showed that transitivity is equivalent to the unique ergodicity on compact subsets of a linearisation disc.
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Numerical Methods With Engineering Applications and Their Visual Analysis via Polynomiography
TL;DR: In this paper, the authors presented polynomiography using newly constructed root-finding algorithms for the solution of non-linear equations, which are two-step predictor-corrector methods.
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Hausdorff measure of escaping and Julia sets for bounded-type functions of finite order
TL;DR: In this paper, it was shown that the escaping sets and Julia sets of bounded type transcendental entire functions of order ρ → ∞ become smaller as ρ ∞ to ∞ and their Hausdorff measures are infinite with respect to the gauge function.
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Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
B. Campos,Jordi Canela,P. Vindel +2 more
TL;DR: This paper uses the criterion for the Chebyshev-Halley methods applied to the degree of polynomials to obtain a characterization of the parameters for which all Fatou components are simply connected and, therefore, the Julia set is connected.