{"paper":{"title":"Integral points of bounded degree on the projective line and in dynamical orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Joseph Gunther, Wade Hindes","submitted_at":"2016-07-27T21:52:42Z","abstract_excerpt":"Let $D$ be a non-empty effective divisor on $\\mathbb{P}^1$. We show that when ordered by height, any set of $(D,S)$-integral points on $\\mathbb{P}^1$ of bounded degree has relative density zero. We then apply this to arithmetic dynamics: let $\\varphi(z)\\in \\overline{\\mathbb{Q}}(z)$ be a rational function of degree at least two whose second iterate $\\varphi^2(z)$ is not a polynomial. We show that as we vary over points $P\\in\\mathbb{P}^1(\\overline{\\mathbb{Q}})$ of bounded degree, the number of algebraic integers in the forward orbit of $P$ is absolutely bounded and zero on average."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08272","kind":"arxiv","version":1},"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"}