Abstract

We prove that for typical self-similar iterated function systems satisfying the transversality condition the number of intersections of cylinders of a given size is for many sizes nearly as small as possible. This implies a result of Solomyak on the absolute continuity of the natural measure and a result of Peres, Simon and Solomyak on the positivity of the packing measure.

Mathematical Subject Classification

Primary: 37C45

Authors