{
  "id": "cond-mat/0312683",
  "version": "v1",
  "published": "2003-12-29T17:46:46.000Z",
  "updated": "2003-12-29T17:46:46.000Z",
  "title": "Two-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics",
  "authors": [
    "Ernesto P. Borges",
    "Ugur Tirnakli"
  ],
  "comment": "Communication at NEXT2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, Villasimius (Cagliari) Italy, 21-28 September 2003. Submitted to Physica A. Elsevier Latex, 8 pages, 6 eps figures",
  "journal": "Physica A 340 227--233 (2004)",
  "doi": "10.1016/j.physa.2004.04.011",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The sensitivity to initial conditions and relaxation dynamics of two-dimensional maps are analyzed at the edge of chaos, along the lines of nonextensive statistical mechanics. We verify the dual nature of the entropic index for the Henon map, one ($q_{sen}<1$) related to its sensitivity to initial conditions properties, and the other, graining-dependent ($q_{rel}(W)>1$), related to its relaxation dynamics towards its stationary state attractor. We also corroborate a scaling law between these two indexes, previously found for $z$-logistic maps. Finally we perform a preliminary analysis of a linearized version of the Henon map (the smoothed Lozi map). We find that the sensitivity properties of all these $z$-logistic, Henon and Lozi maps are the same, $q_{sen}=0.2445...$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-29T17:46:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relaxation dynamics",
      "two-dimensional dissipative maps",
      "chaos threshold",
      "sensitivity",
      "lozi map"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "publication": {
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2004,
      "month": "Sep",
      "volume": 340,
      "number": 1,
      "pages": 227
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004PhyA..340..227B"
    }
  }
}