School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Quantization Dimension Estimate for Condensation Systems of Conformal Mappings

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Let μ 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 ∈ ( 0 , + ∞ ) the lower and the upper quantization dimensions of order r of μ are bounded below by the quantization dimension D r ( \gn ) of \gn and bounded above by a unique number \gk r ∈ ( 0 , + ∞ ) where \gk r has a relationship with the temperature function of the thermodynamic formalism that arises in multifractal analysis of μ .


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Real Analysis Exchange