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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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Perturbative Changes of the Nature of Invariant Varieties for Some Higher Dimensional Integrable Maps
Noriko Saitoh,Satoru Saito +1 more
TL;DR: In this paper, it was shown that all quasi periodic orbits also form an invariant variety if the map can be reduced to a set of Mobius maps using the invariants.
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Zeros of derivatives of meromorphic functions with one pole
TL;DR: In this paper, it was shown that a polynomial of degree not exceeding n+1 has only red zeros for all k ≥ 0 if and only if f and f′ have only real zeros.
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An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable
Daniel S. Graça,Ning Zhong +1 more
TL;DR: In this article, it was shown that one cannot compute the basins of attraction of even very regular systems, namely analytic systems with hyperbolic asymptotically stable equilibrium points.
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Hausdorff measure of escaping and Julia sets for bounded type functions of finite order
TL;DR: In this paper, it was shown that the escaping sets and Julia sets of bounded type transcendental entire functions of order ρ → ∞ become smaller as ρ ∞ to ∞ and their Hausdorff measures are infinite with respect to the gauge function.
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Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps
TL;DR: In this article, it was shown that every Cantor set of circles as the Julia set of a non-hyperbolic rational map must be quasisymmetric equivalent to Julia sets of one map in these families for suitable parameters.