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2012/2013 Quantization Dimension Estimate for Condensation Systems of Conformal Mappings
Mrinal Kanti Roychowdhury
Real Anal. Exchange 38(2): 317-336 (2012/2013).


Let \(\mu\) be the attracting measure of a condensation system consisting of a finite system of conformal mappings associated with a probability measure \(\gn\) which is the image measure of an ergodic measure with bounded distortion. We have shown that for a given \(r\in (0,+\infty)\) the lower and the upper quantization dimensions of order \(r\) of \(\mu\) are bounded below by the quantization dimension \(D_r(\gn)\) of \(\gn\) and bounded above by a unique number \(\gk_r\in (0, +\infty)\) where \(\gk_r\) has a relationship with the temperature function of the thermodynamic formalism that arises in multifractal analysis of \(\mu\).


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Mrinal Kanti Roychowdhury. "Quantization Dimension Estimate for Condensation Systems of Conformal Mappings." Real Anal. Exchange 38 (2) 317 - 336, 2012/2013.


Published: 2012/2013
First available in Project Euclid: 27 June 2014

zbMATH: 1298.28022
MathSciNet: MR3261880

Primary: 26A04 , 28A80
Secondary: 60D05 , 94A15

Keywords: ergodic measure with bounded distortion , inhomogeneous self-conformal measure , Quantization dimension , temperature function

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 2 • 2012/2013
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