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Creators/Authors contains: "Urbański, Mariusz"

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  1. ; ; (, Mathematische Annalen)
    We show that any dynamics on any planar set S, discrete in some domain D, can be realized by the postcritical dynamics of a function holomorphic in D, up to a small perturbation. A key step in the proof, and a result of independent interest, is that any planar domain D can be equilaterally triangulated with triangles whose diameters tend to 0 at any prescribed rate near the boundary. When D is the whole plane, the dynamical result was proved in "Prescribing the Postsingular Dynamics of Meromorphic Functions", by Bishop and Lazebnik by a different method (QC folding). 
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