Real Analysis Exchange

Finer diophantine and regularity properties of 1-dimensional parabolic IFS

Mariusz Urbański

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 143-164.

Dates
First available in Project Euclid: 5 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.rae/1149516811

Mathematical Reviews number (MathSciNet)
MR2218195

Zentralblatt MATH identifier
1160.37312

Subjects
Primary: 11J99: None of the above, but in this section
Secondary: 28A78: Hausdorff and packing measures 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

Keywords
extremal measures parabolic IFS Hausdorff measures conformal measures not very well and badly approximable numbers extendable systems doubling property

Citation

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


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References

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