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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Siegel discs, Herman rings and the Arnold family
TL;DR: In this paper, it was shown that for every Brjuno rotation number there exists an analytically linearizable element of the Arnold family and that the rotation number of such an element satisfies the condition.
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Mating quadratic maps with the modular group
TL;DR: In this paper, Bullett and Penrose showed that every member of the family with a in the connectedness locus is a mating between the modular group and rational maps in the parabolic quadratic family.
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Laplace operators on fractals and related functional equations
TL;DR: In this article, the authors give an overview over the application of functional equations, namely the classical Poincare and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals.
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Schreier spectrum of the Hanoi Towers group on three pegs
Rostislav Grigorchuk,Zoran Sunic +1 more
TL;DR: In this article, finite dimensional representations of the Hanoi Towers group are used to calculate the spectra of the finite graphs associated to the Haoi Towers Game on three pegs (the group serves as a renorm group for the game).
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Dynamics of a new family of iterative processes for quadratic polynomials
TL;DR: This work proves that the coefficients of the aforementioned family of iterative processes can be written in terms of the Catalan numbers, and makes an incursion into its dynamical behavior.