Geometric measures for parabolic rational maps

M. Denker, M. Urbański

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

Let h denote the Hausdorff dimension of the Julia set J(T) of a parabolic rational map T. In this paper we prove that (after normalisation) the h-conformal measure on J(T) equals the h-dimensional Hausdorff measure Hh on J(T), if h ≥ 1, and equals the h-dimensional packing measure Πh on J(T), if h ≤ 1. Moreover, if h < 1, then Hh = 0 and, if h > 1, then Πh(J(T)) = ∞.

Original languageEnglish (US)
Pages (from-to)53-66
Number of pages14
JournalErgodic Theory and Dynamical Systems
Volume12
Issue number1
DOIs
StatePublished - Mar 1992

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Geometric measures for parabolic rational maps'. Together they form a unique fingerprint.

Cite this