Generic behavior of iterated function systems with overlaps

Michał Rams

Vol. 218 (2005), No. 1, 173–186

DOI: 10.2140/pjm.2005.218.173

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 2000

Primary: 37C45

Milestones

Received: 26 April 2002

Published: 1 January 2005