{
  "id": "1311.3199",
  "version": "v1",
  "published": "2013-11-13T16:38:50.000Z",
  "updated": "2013-11-13T16:38:50.000Z",
  "title": "Invariant quadrics and orbits for a family of rational systems of difference equations",
  "authors": [
    "Ignacio Bajo"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the existence of invariant quadrics for a class of systems of difference equations in ${\\mathbb R}^n$ defined by linear fractionals sharing denominator. Such systems can be described in terms of some square matrix $A$ and we prove that there is a correspondence between non-degenerate invariant quadrics and solutions to a certain matrix equation involving $A$. We show that if $A$ is semisimple and the corresponding system admits non-degenerate quadrics, then every orbit of the dynamical system is contained either in an invariant affine variety or in an invariant quadric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-13T16:38:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "difference equations",
      "rational systems",
      "corresponding system admits non-degenerate quadrics",
      "non-degenerate invariant quadrics",
      "linear fractionals sharing denominator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.3199B"
    }
  }
}