{"paper":{"title":"An Equidistribution Result For Dynamical Systems on the Berkovich Projective Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Kenneth Jacobs","submitted_at":"2014-09-16T21:23:34Z","abstract_excerpt":"Let $K$ be a complete, algebraically closed, non-Archimedean valued field, and let $\\phi\\in K(z)$ with $\\textrm{deg}(\\phi) \\geq 2$. In this paper we consider the family of functions $\\textrm{ordRes}_{\\phi^n}(x)$, which measure the resultant of $\\phi^n$ at points $x$ in $\\textbf{P}^1_{\\textrm{K}}$, the Berkovich projective line, and show that they converge locally uniformly to the diagonal values of the Arakelov-Green's function $g_{\\mu_{\\phi}}(x,x)$ attached to the canonical measure of $\\phi$. Following this, we are able to prove an equidistribution result for Rumely's crucial measures $\\nu_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4808","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}