A classification of bicritical dynamic portraits

Edgar Saenz; Dheemanth Samji

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arXiv · 2608.13850

A classification of bicritical dynamic portraits

Edgar Saenz·Dheemanth Samji

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Abstract

The dynamic of a rational map $f:\widehat{\mathbb C}\to \widehat{\mathbb C}$ is determined by the forward orbits of its critical points. Such a map is called {\em postcritically finite} if every critical point has finite forward orbit, or equivalently, if every critical point eventually maps into a periodic cycle. These orbits can be encoded in a finite directed graph called a {\em dynamic portrait}. In this work, we classify which abstract bicritical dynamic portraits of degree $d\geq2$ with at least 4 postcritical points are realizable exclusively by rational Thurston maps.

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Edgar Saenz, Dheemanth Samji. 2026-08-14. A classification of bicritical dynamic portraits. https://arxiv.org/abs/2608.13850

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