{
  "id": "cond-mat/0205356",
  "version": "v2",
  "published": "2002-05-16T22:16:52.000Z",
  "updated": "2002-09-11T14:03:04.000Z",
  "title": "Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: rigorous nonextensive solutions",
  "authors": [
    "F. Baldovin",
    "A. Robledo"
  ],
  "comment": "latex, 4 figures. Updated references and some general presentation improvements. To appear published in Europhysics Letters",
  "journal": "Europhys. Lett. {\\bf 60}, 518 (2002).",
  "doi": "10.1209/epl/i2002-00249-7",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Using the Feigenbaum renormalization group (RG) transformation we work out exactly the dynamics and the sensitivity to initial conditions for unimodal maps of nonlinearity $\\zeta >1$ at both their pitchfork and tangent bifurcations. These functions have the form of $q$-exponentials as proposed in Tsallis' generalization of statistical mechanics. We determine the $q$-indices that characterize these universality classes and perform for the first time the calculation of the $q$-generalized Lyapunov coefficient $\\lambda_{q} $. The pitchfork and the left-hand side of the tangent bifurcations display weak insensitivity to initial conditions, while the right-hand side of the tangent bifurcations presents a `super-strong' (faster than exponential) sensitivity to initial conditions. We corroborate our analytical results with {\\em a priori} numerical calculations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-09-11T14:03:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial conditions",
      "one-dimensional nonlinear maps",
      "rigorous nonextensive solutions",
      "tangent bifurcations display weak insensitivity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}