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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Conjugation of Rational Functions to Power Functions and Applications to Iteration
TL;DR: In this paper, the authors investigate the normalization of rational functions, reducing in the sense of conjugation to monomials or more general power functions, by computing minimal irreducible decomposition of algebraic varieties.
Journal ArticleDOI
Dynamical analytic multifunctions
TL;DR: In this paper, the authors list different examples of analytic dependence on some parameters of Julia type sets or attractors of (generated) iterated function systems, and show that these depend on the type sets themselves.
Book ChapterDOI
Integral Points on Elliptic Curves
TL;DR: In this article, the authors prove a theorem of Siegel which says that there are only finitely many rational points in an elliptic curve with integral coordinates that can be found using Diophantine approximation.
Posted Content
Real-analyticity of hausdorff dimension of julia sets along the parabolic arcs of the multicorns
TL;DR: Mukherjee et al. as mentioned in this paper studied the connect-edness loci of unicritical anti-polynomials, known as the multicorns, and proved a regularity property of the Hausdor dimension of the Julia sets on the per-sistently parabolic part of these parameter spaces.
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Fractal Properties of Magic State Distillation
TL;DR: This work shows that if you lift this one-parameter restriction and embrace the complexity, distillation exhibits fractal properties, and it is demonstrated that some protocols are more effective when not restricted.