Real Analysis Exchange
- Real Anal. Exchange
- Volume 38, Number 2 (2012), 317-336.
Quantization Dimension Estimate for Condensation Systems of Conformal Mappings
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 \(\mu\).
Real Anal. Exchange, Volume 38, Number 2 (2012), 317-336.
First available in Project Euclid: 27 June 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 28A80: Fractals [See also 37Fxx] 26A04
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 94A15: Information theory, general [See also 62B10, 81P94]
Roychowdhury, Mrinal Kanti. Quantization Dimension Estimate for Condensation Systems of Conformal Mappings. Real Anal. Exchange 38 (2012), no. 2, 317--336. https://projecteuclid.org/euclid.rae/1403894895