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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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Möbius disjointness conjecture for local dendrite maps
TL;DR: In this paper, it was shown that the M\\obius disjointness conjecture holds for graph maps and for all monotone local dendrite maps and that this also holds for continuous map on certain class of dendrites.
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Powers in orbits of rational functions: cases of an arithmetic dynamical Mordell-Lang conjecture
TL;DR: In this paper, it was shown that the index set of a rational function over a finitely generated field of characteristic zero is a union of finitely many arithmetic progressions, where π is the $n$th iterate of π and π ∆ is any map Mobius-conjugate over π to π.
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Criteria for the density of the graph of the entropy map restricted to ergodic states
TL;DR: In this paper, the authors consider a non-uniquely ergodic dynamical system given by a -action (or -action) on a nonempty compact metrisable space, for some.
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Ensembles d'unicité pour les polynômes
TL;DR: In this paper, the authors consider the problem of finding constant polynomials f and g such that f −1 (E) = g − 1 (E), where E ⊂ C is a compact set of positive logarithmic capacity.
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Generalized baby Mandelbrot sets adorned with halos in families of rational maps
TL;DR: In this paper, the authors considered the case when n is not necessarily equal to d and showed that there are n-1 small copies of the Mandelbrot set symmetrically located around the origin in the parameter λ-plane.