{
  "id": "math/9303209",
  "version": "v1",
  "published": "1993-03-20T00:00:00.000Z",
  "updated": "1993-03-20T00:00:00.000Z",
  "title": "Accessability of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps",
  "authors": [
    "Feliks Przytycki"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if $A$ is completely invariant (i.e. $f^{-1}(A)=A$), and if $\\mu$ is an arbitrary $f$-invariant measure with positive Lyapunov exponents on the boundary of $A$, then $\\mu$-almost every point $q$ in the boundary of $A$ is accessible along a curve from $A$. In fact we prove the accessability of every \"good\" $q$ i.e. such $q$ for which \"small neighbourhoods arrive at large scale\" under iteration of $f$. This generalizes Douady-Eremenko-Levin-Petersen theorem on the accessability of periodic sources.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-03-20T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive lyapunov exponents",
      "invariant measure",
      "holomorphic maps",
      "typical points",
      "accessability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993math......3209P"
    }
  }
}