{
  "id": "1307.3205",
  "version": "v2",
  "published": "2013-07-11T18:25:18.000Z",
  "updated": "2014-01-12T12:26:10.000Z",
  "title": "Arithmetic dynamics on smooth cubic surfaces",
  "authors": [
    "Solomon Vishkautsan"
  ],
  "comment": "22 pages changes in v2: * major streamlining + many fixes to typos * correction to Corollary in Section 8",
  "journal": "New York J. Math. 20 (2014), 1--25, http://nyjm.albany.edu/j/2014/20-1.html",
  "categories": [
    "math.NT",
    "math.AG",
    "math.DS"
  ],
  "abstract": "We study dynamical systems induced by birational automorphisms on smooth cubic surfaces defined over a number field $K$. In particular we are interested in the product of non-commuting birational Geiser involutions of the cubic surface. We present results describing the sets of $K$ and $\\bar{K}$-periodic points of the system, and give a necessary and sufficient condition for a dynamical local-global property called strong residual periodicity. Finally, we give a dynamical result relating to the Mordell--Weil problem on cubic surfaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-12T12:26:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P35",
      "37P55",
      "37P05"
    ],
    "keywords": [
      "arithmetic dynamics",
      "strong residual periodicity",
      "non-commuting birational geiser involutions",
      "number field",
      "smooth cubic surfaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.3205V"
    }
  }
}