We show upper estimates of the concentration and thin dimensions of measures invariant with respect to families of transformations. These estimates are proved under the assumption that the transformations have a squeezing property which is more general than the Lipschitz condition. These results are in the spirit of a paper by A. Lasota and J. Traple [Chaos Solitons Fractals 28 (2006)] and generalize the classical Moran formula.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-8,
author = {H. Gacki and A. Lasota and J. Myjak},
title = {Upper Estimate of Concentration and Thin Dimensions of Measures},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {57},
year = {2009},
pages = {149-162},
zbl = {1175.37028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-8}
}
H. Gacki; A. Lasota; J. Myjak. Upper Estimate of Concentration and Thin Dimensions of Measures. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 149-162. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-2-8/