Hausdorff measures on Julia sets of subexpanding rational maps

M. Denker, M. Urbański

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11 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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