Real Analysis Exchange
- Real Anal. Exchange
- Volume 31, Number 1 (2005), 143-164.
Finer diophantine and regularity properties of 1-dimensional parabolic IFS
Recall that a Borel probability measure $\mu$ on $\R$ is called extremal if $\mu$-almost every number in $\R$ is not very well approximable. In this paper, we prove extremality (and implying it the exponentially fast decay property (efd)) of conformal measures induced by $1$-dimensional finite parabolic iterated function systems. We also investigate the doubling property of these measures and we estimate from below the Hausdorff dimension of the limit sets of such iterated systems.
Real Anal. Exchange, Volume 31, Number 1 (2005), 143-164.
First available in Project Euclid: 5 June 2006
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Urbański, Mariusz. Finer diophantine and regularity properties of 1-dimensional parabolic IFS. Real Anal. Exchange 31 (2005), no. 1, 143--164. https://projecteuclid.org/euclid.rae/1149516811