Recurrent critical points and typical limit sets of rational maps

Academic Article

Abstract

  • We consider a rational map f : Ĉ →Ĉ of the Riemann sphere with normalized Lebesgue measure μ and show that if there is a subset of the Julia set J(f) of positive μ-measure whose points have limit sets not contained in the union of the limit sets of recurrent critical points, then ω(x) = Ĉ = J(f) for μ-a.e. point x and f is conservative, ergodic and exact. © 1999 American Mathematical Society.
  • Author List

  • Blokh AM; Mayer JC; Oversteegen LG
  • Start Page

  • 1215
  • End Page

  • 1220
  • Volume

  • 127
  • Issue

  • 4