Equilateral triangulations and the postcritical dynamics of meromorphic functions

Christopher J. Bishop; Kirill Lazebnik; Mariusz Urbański

doi:10.1007/s00208-022-02507-4

Equilateral triangulations and the postcritical dynamics of meromorphic functions

Christopher J. Bishop
, Kirill Lazebnik
, Mariusz Urbański

Mathematics

University of North Texas

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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 → 0 (at any prescribed rate) near ∂D.

Original language	English
Pages (from-to)	1777-1818
Number of pages	42
Journal	Mathematische Annalen
Volume	387
Issue number	3-4
DOIs	https://doi.org/10.1007/s00208-022-02507-4
State	Published - Dec 2023

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title = "Equilateral triangulations and the postcritical dynamics of meromorphic functions",

abstract = "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 → 0 (at any prescribed rate) near ∂D.",

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AU - Bishop, Christopher J.

AU - Lazebnik, Kirill

AU - Urbański, Mariusz

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N2 - 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 → 0 (at any prescribed rate) near ∂D.

AB - 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 → 0 (at any prescribed rate) near ∂D.

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JF - Mathematische Annalen

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Equilateral triangulations and the postcritical dynamics of meromorphic functions

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