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2 Bulletin of the Polish Academy of Sciences. Mathematics

2 Roychowdhury M. K.

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Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

100%

Roychowdhury M. K.

Bulletin of the Polish Academy of Sciences. Mathematics

2013

tom Vol. 61, no 1

35--45

We consider an inhomogeneous measure μ with the inhomogeneous part a self-similar measure ν, and show 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 Dr(ν) of ν and bounded above by a unique number κr∈(0,∞), related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of μ.

Quantization dimension function and ergodic measure with bounded distortion

100%

Roychowdhury M. K.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

tom Vol. 57, no 3-4

251-262

The quantization dimension function for the image measure of a shift-invariant ergodic measure with bounded distortion on a self-conformal set is determined, and its relationship to the temperature function of the thermodynamic formalism arising in multifractal analysis is established.