Generic behavior of iterated function systems with overlaps

Abstract

MICHAŁ RAMSWe 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.