{
  "id": "1803.03928",
  "version": "v1",
  "published": "2018-03-11T08:45:33.000Z",
  "updated": "2018-03-11T08:45:33.000Z",
  "title": "Density of orbits of endomorphisms of commutative linear algebraic groups",
  "authors": [
    "Dragos Ghioca",
    "Fei Hu"
  ],
  "comment": "New York Journal of Mathematics (to appear)",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove a conjecture of Medvedev and Scanlon for endomorphisms of connected commutative linear algebraic groups $G$ defined over an algebraically closed field $\\mathbb{k}$ of characteristic $0$. That is, if $\\Phi\\colon G\\longrightarrow G$ is a dominant endomorphism, we prove that one of the following holds: either there exists a non-constant rational function $f\\in \\mathbb{k}(G)$ preserved by $\\Phi$ (i.e., $f\\circ \\Phi = f$), or there exists a point $x\\in G(\\mathbb{k})$ whose $\\Phi$-orbit is Zariski dense in $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-11T08:45:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P15",
      "20G15",
      "32H50"
    ],
    "keywords": [
      "connected commutative linear algebraic groups",
      "non-constant rational function",
      "dominant endomorphism",
      "zariski dense",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}