{
  "id": "math/0507543",
  "version": "v2",
  "published": "2005-07-26T17:14:18.000Z",
  "updated": "2006-10-16T16:10:20.000Z",
  "title": "Markov extensions and lifting measures for complex polynomials",
  "authors": [
    "Henk Bruin",
    "Mike Todd"
  ],
  "comment": "Some changes have been made, in particular to Sections 2 and 3, to clarify the exposition. Typos have been corrected and references updated",
  "journal": "Ergodic Theory Dynam. Systems 27 (2007) 743-768",
  "categories": [
    "math.DS"
  ],
  "abstract": "For polynomials $f$ on the complex plane with a dendrite Julia set we study invariant probability measures, obtained from a reference measure. To do this we follow Keller in constructing canonical Markov extensions. We discuss ``liftability'' of measures (both $f$-invariant and non-invariant) to the Markov extension, showing that invariant measures are liftable if and only if they have a positive Lyapunov exponent. We also show that $\\delta$-conformal measure is liftable if and only if the set of points with positive Lyapunov exponent has positive measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-16T16:10:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37F10",
      "37F35",
      "37C40"
    ],
    "keywords": [
      "complex polynomials",
      "lifting measures",
      "positive lyapunov exponent",
      "study invariant probability measures",
      "dendrite julia set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7543B"
    }
  }
}