{"paper":{"title":"The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DS","authors_text":"Junyi Xie","submitted_at":"2015-10-26T21:14:05Z","abstract_excerpt":"In this paper we prove the following theorem. Let $f:\\mathbb{A}^2\\rightarrow \\mathbb{A}^2$ be a dominate polynomial endomorphisms defined over an algebraically closed field $k$ of characteristic $0$. If there are no nonconstant rational function $g:\\mathbb{A}^2-rightarrow \\mathbb{P}^1$ satisfying $g\\circ f=g$, then there exists a point $p\\in \\mathbb{A}^2(k)$ whose orbit under $f$ is Zariski dense in $\\mathbb{A}^2$.\n  This result gives us a positive answer to a conjecture of Amerik, Bogomolov and Rovinsky ( and Zhang) for polynomial endomorphisms on the affine plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07684","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"}