Dimension of slices of Sierpiński-like carpets

Abstract

We investigate the dimension of intersections of the Sierpinski-like carpets with lines. We show a sufficient condition that for a fixed rational slope the dimension of almost every intersection w.r.t the natural measure is strictly greater than s− 1, and almost every intersection w.r.t the Lebesgue measure is strictly less than s − 1, where s is the Hausdorff dimension of the carpet. Moreover, we give partial multifractal spectra for the Hausdorff and packing dimension of slices. Mathematics Subject Classification (2010). 28A80; 28A78.