Dimensions of slices through the Sierpiński gasket. Issue 3 (4th March 2022) - Nakajima, Yuto
Abstract : We discuss the intersections of the d -dimensional Sierpiński gasket with ( d − 1 ) -dimensional hyperplanes in a particular fixed direction. We give the values of the Hausdorff dimension, the lower box dimension, the upper box dimension, and the packing dimension of each slice and determine the criterion for which the Hausdorff dimension of the slice takes Marstrand's value. In order to investigate the slices, we improve the theory of non-autonomous conformal iterated function systems.