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arXiv · 1902.00938

Local dimensions and quantization dimensions in dynamical systems

Mrinal Kanti Roychowdhury·Bilel Selmi
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Abstract

Let $\mu$ be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of $\mathbb R^k$. We study the Hausdorff and the packing dimensions, and the quantization dimensions of $\mu$ with respect to the geometric mean error. The results establish the connections with various dimensions of the measure $\mu$, and generalize many known results about local dimensions and quantization dimensions of measures.

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Mrinal Kanti Roychowdhury, Bilel Selmi. 2019-02-03. Local dimensions and quantization dimensions in dynamical systems. https://arxiv.org/abs/1902.00938

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