{
  "id": "cond-mat/9702204",
  "version": "v1",
  "published": "1997-02-22T12:15:24.000Z",
  "updated": "1997-02-22T12:15:24.000Z",
  "title": "Scale Invariance in Percolation Theory and Fractals",
  "authors": [
    "M. V. Entin",
    "G. M. Entin"
  ],
  "comment": "LaTeX file and 2 PostScripts with 6 fig.",
  "journal": "JETP Lett., Vol. 64, No. 6, 25 Sept. 1996",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "The properties of the similarity transformation in percolation theory in the complex plane of the percolation probability are studied. It is shown that the percolation problem on a two-dimensional square lattice reduces to the Mandelbrot transformation, leading to a fractal behavior of the percolation probability in the complex plane. The hierarchical chains of impedances, reducing to a nonlinear mapping of the impedance space onto itself, are studied. An infinite continuation of the procedure leads to a fixed point. It is shown that the number of steps required to reach a neighborhood of this point has a fractal distribution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-02-22T12:15:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "percolation theory",
      "scale invariance",
      "complex plane",
      "two-dimensional square lattice reduces",
      "percolation probability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997cond.mat..2204E"
    }
  }
}