Attractors for graph critical rational maps

Academic Article

Abstract

  • We call a rational map f graph critical if any critical point either belongs to an invariant finite graph G, or has minimal limit set, or is nonrecurrent and has limit set disjoint from G. We prove that, for any conformal measure, either for almost every point of the Julia set J(f) its limit set coincides with J(f), or for almost every point of J(f) its limit set coincides with the limit set of a critical point of f.
  • Digital Object Identifier (doi)

    Author List

  • Blokh A; Misiurewicz M
  • Start Page

  • 3639
  • End Page

  • 3661
  • Volume

  • 354
  • Issue

  • 9