{
  "id": "math/0611297",
  "version": "v4",
  "published": "2006-11-09T23:26:00.000Z",
  "updated": "2009-03-10T20:07:42.000Z",
  "title": "Dynamics of Rational Surface Automorphisms: Linear Fractional Recurrences",
  "authors": [
    "Eric Bedford",
    "Kyounghee Kim"
  ],
  "comment": "24 pages, 7 figures, A companion Mathematica notebook is available at: http://www.math.fsu.edu/~kim/",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the family $f_{a,b}(x,y)=(y,(y+a)/(x+b))$ of birational maps of the plane and the parameter values $(a,b)$ for which $f_{a,b}$ gives an automorphism of a rational surface. In particular, we find values for which $f_{a,b}$ is an automorphism of positive entropy but no invariant curve. The Main Theorem: If $f_{a,b}$ is an automorphism with an invariant curve and positive entropy, then either (1) $(a,b)$ is real, and the restriction of $f$ to the real points has maximal entropy, or (2) $f_{a,b}$ has a rotation (Siegel) domain.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-03-10T20:07:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F99",
      "32M99",
      "32H50"
    ],
    "keywords": [
      "linear fractional recurrences",
      "rational surface automorphisms",
      "invariant curve",
      "positive entropy",
      "main theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11297B"
    }
  }
}