2022/02/04 by Christopher J. Bishop, Bishop, Christopher J., Kirill Lazebnik +3
Computer Science · Mathematics · #30D05 #30D30 #37F10 #Complex Variables (math.CV) #Computational Geometry and Mesh Generation #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2202.02410
openalex publication_date 2022/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.