Multifractal spectra of Moran measures without local dimension
Dynamical Systems
2020-01-08 v1
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 (-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.
Keywords
Cite
@article{arxiv.1811.05075,
title = {Multifractal spectra of Moran measures without local dimension},
author = {Zhihui Yuan},
journal= {arXiv preprint arXiv:1811.05075},
year = {2020}
}