Hausdorff measures on Julia sets of subexpanding rational maps

M. Denker, M. Urbański

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Let h be the Hausdorff dimension of the Julia set J(R) of a Misiurewicz's rational map R : {Mathematical expression} (subexpanding case). We prove that the h-dimensional Hausdorff measure H h on J(R) is finite, positive and the only h-conformal measure for R : {Mathematical expression} up to a multiplicative constant. Moreover, we show that there exists a unique R-invariant measure on J(R) equivalent to H h .

Original languageEnglish (US)
Pages (from-to)193-214
Number of pages22
JournalIsrael Journal of Mathematics
Volume76
Issue number1-2
DOIs
StatePublished - Oct 1 1991

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Rational Maps
Hausdorff Measure
Julia set
Conformal Measure
Hausdorff Dimension
Invariant Measure
Multiplicative

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Denker, M. ; Urbański, M. / Hausdorff measures on Julia sets of subexpanding rational maps. In: Israel Journal of Mathematics. 1991 ; Vol. 76, No. 1-2. pp. 193-214.
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Hausdorff measures on Julia sets of subexpanding rational maps. / Denker, M.; Urbański, M.

In: Israel Journal of Mathematics, Vol. 76, No. 1-2, 01.10.1991, p. 193-214.

Research output: Contribution to journalArticle

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