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Quantization dimension for a generalized inhomogeneous bi-Lipschitz iterated function system
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DOI：10.1016/j.chaos.2026.118321.png)
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Abstract
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• We show that the quantization dimension of an invariant measure associated with a condensation system is bounded above by the maximum of the quantization dimension of the invariant measure associated with the homogeneous part and the condensation part. • It generalizes the results present in the literature, where the condensation part is also generated by a self-similar IFS. • We consider the condensation part to be an image measure of an ergodic measure with bounded distortion. • We determine the optimal quantization for an infinite discrete distribution. • Give an example which shows that the quantization dimension of a Borel probability measure can be positive with zero quantization co-efficient.
Keywords:
quantization dimension
inhomogeneous iterated function system
condensation system
ergodic measure
bi-Lipschitz transformation
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