Attractors and recurrence for dendrite-critical polynomials

Academic Article

Abstract

  • We call a rational map f dendrite-critical if all its recurrent critical points either belong to an invariant dendrite D or have minimal limit sets. We prove that if f is a dendrite-critical polynomial, then for any conformal measure μ either for almost every point its limit set coincides with the Julia set of f, or for almost every point its limit set coincides with the limit set of a critical point c of f. Moreover, if μ is non-atomic, then c can be chosen to be recurrent. A corollary is that for a dendrite-critical polynomial and a non-atomic conformal measure the limit set of almost every point contains a critical point. © 2004 Elsevier Inc. All rights reserved.
  • Digital Object Identifier (doi)

    Author List

  • Blokh A; Misiurewicz M
  • Start Page

  • 567
  • End Page

  • 588
  • Volume

  • 306
  • Issue

  • 2