Work

Resultant measures and minimal resultant loci for non-archimedean polynomial dynamics

Year: 2025

Type: article

Abstract: We compute the resultant measures for the iterations Pj, j≥1, of a polynomial P of degree >1 on the nth level Trucco trees Γn, n≥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→∞, and establish a uniform stationarity of Rumely’s minimal resultant loci of Pj or equivalently that of the potential semistable reduction loci of Pj as j→∞. We also establish several equidistribution results for the resultant measures themselves as n→∞.

Source: Acta Arithmetica

DOI: 10.4064/aa240902-1-2

Authors: Hongming Nie, Yûsuke Okuyama

Institutions: Stony Brook University, Kyoto Institute of Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: Israel Science Foundation, Stony Brook University, Japan Society for the Promotion of Science

Awards: Analytic studies of the moduli and irrationally indifferent cycles in higher dimensional complex and non-archimedean dynamics, 複素および非アルキメデス的力学系の無理的中立周期系および退化と分岐の解析的研究, Bifurcation and renormalization of real and complex dynamical systems