{"paper":{"title":"Invariant varieties for polynomial dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.LO","math.NT"],"primary_cat":"math.DS","authors_text":"Alice Medvedev, Thomas Scanlon","submitted_at":"2009-01-15T21:46:51Z","abstract_excerpt":"We study algebraic dynamical systems (and, more generally, $\\sigma$-varieties) $\\Phi:{\\mathbb A}^n_{\\mathbb C} \\to {\\mathbb A}^n_{\\mathbb C}$ given by coordinatewise univariate polynomials by refining a theorem of Ritt. More precisely, we find a nearly canonical way to write a polynomial as a composition of \"clusters\". Our main result is an explicit description of the (weakly) skew-invariant varieties. As a special case, we show that if $f(x) \\in {\\mathbb C}[x]$ is a polynomial of degree at least two which is not conjugate to a monomial, Chebyshev polynomial or a negative Chebyshev polynomial,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.2352","kind":"arxiv","version":3},"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"}