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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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Blaschke products and rational functions with Siegel disks
TL;DR: In this paper, it was shown that for any real number ∈ (0; 1) and complex number with | | ≤ 1 which satisfy e2i m 1, there exists a modified Blaschke product B of degree 2m + 1 which has a fixed point of multiplier m at the point at infinity such that the restriction of the Blaschek product B on the unit circle is a critical circle map with rotation number.
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On the Inhomogeneity of the Mandelbrot Set
TL;DR: In this paper, it was shown that the Mandelbrot set is locally conformally inhomogeneous: the only conformal map defined in an open set of polynomials intersecting the Julia sets and satisfying the identity map of the set is the Identity Map.
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Fatou and Julia like sets
TL;DR: For a family of holomorphic functions on an arbitrary domain, this paper introduced Fatou and Julia like sets, and established some interesting properties of these sets. But they did not consider the relation between the two sets.
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Hierarchical pinning models, quadratic maps and quenched disorder
TL;DR: In this article, a hierarchical model of polymer pinning in the presence of quenched disorder is considered, which can be reinterpreted as an infinite dimensional dynamical system with random initial condition (the disorder).
Exterior discrete semi-flows
TL;DR: In this article, the authors study the notion of exterior discrete semi-flow and apply it to the analysis of iterative processes induced by some numerical methods. But their main focus is on the problem of finding the basins of attraction of fixed and m-periodic points associated with a rational map defined on the surface of the sphere S2.