{
  "id": "cond-mat/0401128",
  "version": "v1",
  "published": "2004-01-08T18:53:22.000Z",
  "updated": "2004-01-08T18:53:22.000Z",
  "title": "Multifractality and nonextensivity at the edge of chaos of unimodal maps",
  "authors": [
    "E. Mayoral",
    "A. Robledo"
  ],
  "comment": "Contribution to the proceedings of 2nd International Conference on News and Expectations in Thermostatistics (NEXT03), Cagliari, Italy, 21-28/09/2003. Submitted to Physica A",
  "journal": "Physica A 340, 219-226 (2004)",
  "doi": "10.1016/j.physa.2004.04.010",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD"
  ],
  "abstract": "We examine both the dynamical and the multifractal properties at the chaos threshold of logistic maps with general nonlinearity $z>1$. First we determine analytically the sensitivity to initial conditions $\\xi_{t}$. Then we consider a renormalization group (RG) operation on the partition function $Z$ of the multifractal attractor that eliminates one half of the multifractal points each time it is applied. Invariance of $Z$ fixes a length-scale transformation factor $2^{-\\eta}$ in terms of the generalized dimensions $D_{\\beta}$. There exists a gap $\\Delta \\eta $ in the values of $\\eta $ equal to $\\lambda _{q}=1/(1-q)=D_{\\infty}^{-1}-D_{-\\infty}^{-1}$ where $\\lambda_{q}$ is the $q$-generalized Lyapunov exponent and $q$ is the nonextensive entropic index. We provide an interpretation for this relationship - previously derived by Lyra and Tsallis - between dynamical and geometrical properties. Key Words: Edge of chaos, multifractal attractor, nonextensivity",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-08T18:53:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unimodal maps",
      "nonextensivity",
      "multifractality",
      "multifractal attractor",
      "length-scale transformation factor"
    ],
    "tags": [
      "conference paper",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}