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
Citations
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Review of some iterative root-finding methods from a dynamical point of view
TL;DR: In this article, the root-finding iterative methods of Chebyshev, Stirling, and Steffensen were studied from a dynamical point of view applied to complex polynomials.
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On semiconjugation of entire functions
Walter Bergweiler,Aimo Hinkkanen +1 more
TL;DR: In this paper, it was shown that if f satisfies a certain condition, which holds, in particular, if f has no wandering domains, then g−1(J(h))=J(f).
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The Dynamics of Semigroups of Rational Functions I
TL;DR: In this article, a generalisation of the classical theory of the dynamics associated to the iteration of a rational mapping of the Riemann sphere, to the more general setting of the dynamic associated to an arbitrary semigroup of rational mappings is presented.
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The ergodic theory of shrinking targets.
Richard Hill,Sanju Velani +1 more
TL;DR: In this article, a class of well-approximate sets for dynamical systems equipped with a metric are associated with the Julia set, and the Hausdorff dimension of the associated sets is computed.
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Iterated function systems, Ruelle operators, and invariant projective measures
TL;DR: A Fourier-based harmonic analysis for a class of discrete dynamical systems which arise from Iterated Function Systems (IFS) (X,μ) is introduced, based on a Markov process on certain paths.