{
  "id": "math/0610969",
  "version": "v1",
  "published": "2006-10-31T14:10:59.000Z",
  "updated": "2006-10-31T14:10:59.000Z",
  "title": "A \"metric\" complexity for weakly chaotic systems",
  "authors": [
    "S. Galatolo"
  ],
  "comment": "15 pages, no figures. Article",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its value is given by a sort of local entropy, this indicator is quite simple to be calculated. We give some example of calculation in nontrivial systems (interval exchanges, piecewise isometries e.g.) and a formula similar to the Ruelle-Pesin one, relating the complexity indicator to some initial condition sensitivity indicators playing the role of positive Lyapunov exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-31T14:10:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35"
    ],
    "keywords": [
      "weakly chaotic systems",
      "complexity indicator",
      "initial condition sensitivity indicators playing",
      "large measure subset",
      "interval exchanges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}