Real Analysis Exchange

Quantization Dimension Estimate for Condensation Systems of Conformal Mappings

Mrinal Kanti Roychowdhury

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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

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894895

Mathematical Reviews number (MathSciNet)
MR3261880

Zentralblatt MATH identifier
1298.28022

Subjects
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]

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

Citation

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


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