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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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Behavior of lacunary series at the natural boundary
Ovidiu Costin,M. Huang +1 more
TL;DR: In this paper, a local theory of Lacunary Dirichlet series of the form ======$\sum\limits_{k=1}^{\infty}c_k\exp(-zg(k)), \Re(z)>0$ as $z$ approaches the boundary $i\RR, under the assumption $g'\to\infty$ and further assumptions on $ck$.
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Polynomial Root-Finding Methods Whose Basins of Attraction Approximate Voronoi Diagram
TL;DR: The results are used to define and prove an infinite layering within each Voronoi cell of a given set of points, whether known implicitly as roots of a polynomial equation, or explicitly via their coordinates.
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Deterministic chaos and fractal entropy scaling in Floquet conformal field theories
TL;DR: The work of DSA, which consisted in designing the project and computing the energy and entanglement evolution for the tent map, was supported by the Russian Science Foundation through Grant No 17-71-20154 and performed at the Steklov Mathematical Institute of Russian Academy of Sciences as discussed by the authors.
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Julia sets of subhyperbolic rational functions
TL;DR: In this article, it was shown that the Julia sets of subhyperbolic rational functions are Jordan curves and that the boundaries of simply connected attracting components of such functions are closed curves.
A monotonicity conjecture for the entropy of Hubbard trees
TL;DR: A monotonicity conjecture for the entropy of Hubbard trees has been proposed in this article, where it is shown that the entropy is monotonically monotonous in the sense of the Dissertation.