{
  "id": "0705.2753",
  "version": "v1",
  "published": "2007-05-18T18:48:46.000Z",
  "updated": "2007-05-18T18:48:46.000Z",
  "title": "Measures related to (e,n)-complexity functions",
  "authors": [
    "Valentin Afraimovich",
    "Lev Glebsky"
  ],
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\\epsilon$ during the time interval n. Behavior of the (e, n)-complexity functions as n goes to infinity is reflected in the properties of special measures. These measures are constructed as limits of atomic measures supported at points of (e,n)-separated sets. We study such measures. In particular, we prove that they are invariant if the (e,n)-complexity function grows subexponentially. Keywords: Topological entropy, complexity functions, separability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-18T18:48:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28C15",
      "37C99"
    ],
    "keywords": [
      "trajectories",
      "borel set",
      "complexity functions",
      "special measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.2753A"
    }
  }
}