Non-Archimedean techniques and dynamical degenerations
Dynamical Systems
2026-05-12 v3 Complex Variables
Abstract
We develop non-Archimedean techniques to analyze the degeneration of a sequence of rational maps of the complex projective line. We provide an alternative to Luo's method which was based on ultra-limits of the hyperbolic 3-space. We build hybrid spaces using Berkovich theory which enable us to prove the convergence of equilibrium measures, and to determine the asymptotics of Lyapunov exponents.
Cite
@article{arxiv.2406.15892,
title = {Non-Archimedean techniques and dynamical degenerations},
author = {Charles Favre and Chen Gong},
journal= {arXiv preprint arXiv:2406.15892},
year = {2026}
}