The multifractal generalizations of Hausdorff dimension and packing dimension are investigated for an invariant subset A of a piecewise monotonic map on the interval. Formulae for the multifractal dimension of an ergodic invariant measure, the essential multifractal dimension of A, and the multifractal Hausdorff dimension of A are derived.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-3-2,
author = {Franz Hofbauer and Peter Raith and Thomas Steinberger},
title = {Multifractal dimensions for invariant subsets of piecewise monotonic interval maps},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {209-232},
zbl = {1051.37011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-3-2}
}
Franz Hofbauer; Peter Raith; Thomas Steinberger. Multifractal dimensions for invariant subsets of piecewise monotonic interval maps. Fundamenta Mathematicae, Tome 177 (2003) pp. 209-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm176-3-2/