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