Israel Journal of Mathematics

, Volume 76, Issue 1, pp 193–214

Hausdorff measures on Julia sets of subexpanding rational maps

  • M. Denker
  • M. Urbański
Article

DOI: 10.1007/BF02782852

Cite this article as:
Denker, M. & Urbański, M. Israel J. Math. (1991) 76: 193. doi:10.1007/BF02782852

Abstract

Leth be the Hausdorff dimension of the Julia setJ(R) of a Misiurewicz’s rational mapR :\(R:\bar {\mathbb{C}} \to \bar {\mathbb{C}}\) (subexpanding case). We prove that theh-dimensional Hausdorff measure Hh onJ(R) is finite, positive and the onlyh-conformal measure forR :\(R:\bar {\mathbb{C}} \to \bar {\mathbb{C}}\) up to a multiplicative constant. Moreover, we show that there exists a uniqueR-invariant measure onJ(R) equivalent to Hh.

Copyright information

© Hebrew University 1991

Authors and Affiliations

  • M. Denker
    • 1
  • M. Urbański
    • 2
  1. 1.Institute of StochasticsUniversity of GöttingenGöttingenGermany
  2. 2.Institute of MathematicsUniversity of ToruńToruńPoland