School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Quantization Dimension Estimate for Condensation Systems of Conformal Mappings

Document Type

Article

Publication Date

2013

Abstract

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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Original published version available at https://projecteuclid.org/journals/real-analysis-exchange/volume-38/issue-2/Quantization-Dimension-Estimate-for-Condensation-Systems-of-Conformal-Mappings/rae/1403894895.full

Publication Title

Real Analysis Exchange

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