{
  "id": "1205.7003",
  "version": "v1",
  "published": "2012-05-31T14:22:51.000Z",
  "updated": "2012-05-31T14:22:51.000Z",
  "title": "Upper and lower bounds for the iterates of order-preserving homogeneous maps on cones",
  "authors": [
    "Philip Chodrow",
    "Cole Franks",
    "Brian Lins"
  ],
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We define upper bound and lower bounds for order-preserving homogeneous of degree one maps on a proper closed cone in $\\R^n$ in terms of the cone spectral radius. We also define weak upper and lower bounds for these maps. For a proper closed cone $C \\subset \\R^n$, we prove that any order-preserving homogeneous of degree one map $f: \\inter C \\rightarrow \\inter C$ has a lower bound. If $C$ is polyhedral, we prove that the map $f$ has a weak upper bound. We give examples of weak upper bounds for certain order-preserving homogeneous of degree one maps defined on the interior of $\\R^n_+$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-31T14:22:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47H07",
      "15B48"
    ],
    "keywords": [
      "lower bound",
      "order-preserving homogeneous maps",
      "weak upper bound",
      "proper closed cone",
      "define upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.7003C"
    }
  }
}