{
  "id": "cond-mat/9708220",
  "version": "v1",
  "published": "1997-08-28T19:12:48.000Z",
  "updated": "1997-08-28T19:12:48.000Z",
  "title": "Fine structure and complex exponents in power law distributions from random maps",
  "authors": [
    "Per Jögi",
    "Didier Sornette",
    "Michael Blank"
  ],
  "comment": "16 pages (double column RevTeX) with 16 (embedded eps) figures, to appear in Physical Review E",
  "journal": "Phys. Rev. E 57 120-134 (1998)",
  "doi": "10.1103/PhysRevE.57.120",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Discrete scale invariance (DSI) has recently been documented in time-to-failure rupture, earthquake processes and financial crashes, in the fractal geometry of growth processes and in random systems. The main signature of DSI is the presence of log-periodic oscillations correcting the usual power laws, corresponding to complex exponents. Log-periodic structures are important because they reveal the presence of preferred scaling ratios of the underlying physical processes. Here, we present new evidence of log-periodicity overlaying the leading power law behavior of probability density distributions of affine random maps with parametric noise. The log-periodicity is due to intermittent amplifying multiplicative events. We quantify precisely the progressive smoothing of the log-periodic structures as the randomness increases and find a large robustness. Our results provide useful markers for the search of log-periodicity in numerical and experimental data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-08-28T19:12:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "power law distributions",
      "complex exponents",
      "fine structure",
      "log-periodic structures",
      "affine random maps"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}