{"paper":{"title":"Iteration and the Minimal Resultant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kenneth Jacobs, Phillip Williams","submitted_at":"2016-08-06T21:07:01Z","abstract_excerpt":"Let $K$ be an algebraically closed field that is complete with respect to a non-Archimedean absolute value, and let $\\varphi\\in K(z)$ have degree $d\\geq 2$. We characterize maps for which the minimal resultant of an iterate $\\varphi^n$ is given by a simple formula in terms of $d$, $n$, and the minimal resultant of $\\varphi$. We show that such maps are precisely those with reduction outside of an indeterminacy locus $I(d)$ and which also have semi-stable reduction for every iterate $\\varphi^n$. We give two equivalent ways of describing such maps, one measure theoretic and the other in terms of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02155","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"}