Geometric measures for parabolic rational maps

Manfred Heinz Denker, M. Urbański

Research output: Contribution to journalArticle

28 Citations (Scopus)

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 - Jan 1 1992

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Rational Maps
Packing Measure
Conformal Measure
Hausdorff Measure
Julia set
Hausdorff Dimension
Normalization
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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Denker, Manfred Heinz ; Urbański, M. / Geometric measures for parabolic rational maps. In: Ergodic Theory and Dynamical Systems. 1992 ; Vol. 12, No. 1. pp. 53-66.
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Geometric measures for parabolic rational maps. / Denker, Manfred Heinz; Urbański, M.

In: Ergodic Theory and Dynamical Systems, Vol. 12, No. 1, 01.01.1992, p. 53-66.

Research output: Contribution to journalArticle

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