Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics
Volume 221 / 2025
Acta Arithmetica 221 (2025), 55-99
MSC: Primary 37P50; Secondary 11S82, 37P05
DOI: 10.4064/aa240902-1-2
Published online: 3 October 2025
Abstract
We compute the resultant measures for the iterations $P^j$, $j\ge 1$, of a polynomial $P$ of degree $ \gt 1$ on the $n$th level Trucco trees $\varGamma _n$, $n\ge 0$, in the Berkovich projective line over a non-archimedean field and also determine their barycenters. As applications, we study the asymptotic of those barycenters as $n\to \infty $, and establish a uniform stationarity of Rumely’s minimal resultant loci of $P^j$ or equivalently that of the potential semistable reduction loci of $P^j$ as $j\to \infty $. We also establish several equidistribution results for the resultant measures themselves as $n\to \infty $.
