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arXiv · 1811.05075

Multifractal spectra of Moran measures without local dimension

Zhihui Yuan
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Abstract

A measure without local dimension is a measure such that local dimension does not exist for any point in its support. In this paper, we construct such a class of Moran measures and study their lower and upper local dimensions. We show that the related "free energy" function ($L^q$-spectrum) does not exist. Nevertheless, we can obtain the full Hausdroff and packing dimension spectra for level sets defined by lower and upper local dimensions. They can be viewed as a generalized multifractal formalism.

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Zhihui Yuan. 2018-11-13. Multifractal spectra of Moran measures without local dimension. https://doi.org/10.1088/1361-6544%2Fab45d7

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