## Real Analysis Exchange

### Quantization Dimension Estimate for Condensation Systems of Conformal Mappings

Mrinal Kanti Roychowdhury

#### Abstract

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 $\mu$.

#### Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 317-336.

Dates
First available in Project Euclid: 27 June 2014