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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Solving the Sextic by Iteration: A Study in Complex Geometry and Dynamics
TL;DR: The Valentiner action of A 6 on P2 is used to develop an iterative algorithm for the solution of the general sextic equation over , analogous to Doyle and McMullen's algorithms for the quintic.
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Metric diophantine approximation in Julia sets of expanding rational maps
Richard Hill,Sanju Velani +1 more
TL;DR: In this article, it was shown that the Hausdorff dimension of Dz 0(f) is the unique positive numbers satisfying the equation P(T,−s(f)), where P is the pressure on the Julia set.
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Newton's method and a class of meromorphic functions without wandering domains
TL;DR: In this article, it was shown that if f ∈ N and if ∞ is among the limit functions of fn in a cycle of periodic domains, then this cycle contains a singularity of f−1.
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Coupled map lattices as computational systems
TL;DR: It is shown that the CML is a valid new model for a parallel deterministic analog machine, but that, in principle, such a CML computer does not generate computations that cannot be reproduced by the standard mathematical models for computing on real numbers.
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Examples of dynamical degree equals arithmetic degree
TL;DR: For algebraic points P of X whose forward orbits are well-defined, there is an analogous (upper) arithmetic degree a_f(P) = limsup h_X(f^n(P))^{1/n), where h is an ample Weil height on X.