Real Analysis Exchange

Quantization Dimension Estimate for Condensation Systems of Conformal Mappings

Mrinal Kanti Roychowdhury

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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

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

First available in Project Euclid: 27 June 2014

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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]

inhomogeneous self-conformal measure ergodic measure with bounded distortion quantization dimension temperature function


Roychowdhury, Mrinal Kanti. Quantization Dimension Estimate for Condensation Systems of Conformal Mappings. Real Anal. Exchange 38 (2012), no. 2, 317--336.

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