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2005-2006 Finer diophantine and regularity properties of 1-dimensional parabolic IFS
Mariusz Urbański
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Real Anal. Exchange 31(1): 143-164 (2005-2006).


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.


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Mariusz Urbański. "Finer diophantine and regularity properties of 1-dimensional parabolic IFS." Real Anal. Exchange 31 (1) 143 - 164, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1160.37312
MathSciNet: MR2218195

Primary: 11J99
Secondary: 28A78 , 37E05

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

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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