For a linear solenoid with two different contraction coefficients and box dimension greater than 2, we give precise formulas for the Hausdorff and packing dimensions. We prove that the packing measure is infinite and give a condition necessary and sufficient for the Hausdorff measure to be positive, finite and equivalent to the SBR measure. We also give analogous results, generalizing [P], for affine IFS in ℝ².
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-7,
author = {Micha\l\ Rams},
title = {Hausdorff and packing measure for thick solenoids},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {193-202},
zbl = {1117.28005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-7}
}
Michał Rams. Hausdorff and packing measure for thick solenoids. Studia Mathematica, Tome 162 (2004) pp. 193-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-7/