On the quantization for self-affine measures on Bedford–McMullen carpets
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For a self-affine measure on a Bedford–McMullen carpet we prove that its quantization dimension of order \(r>0\) exists and determine its exact value. Further, we give various sufficient conditions for the corresponding upper and lower quantization coefficient to be both positive and finite. Finally, we compare the quantization dimension with corresponding quantities derived from the multifractal free energy function and show that—different from conformal systems—they in general do not coincide.
KeywordsQuantization dimension Quantization coefficient Bedford–McMullen carpets Self-affine measures Multifractal formalism
Mathematics Subject Classification28A75 28A80 94A15
S.Z. is supported by National Natural Science Foundation of China No. 11571144 and China Scholarship Council No. 201308320049.
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