Self-similar measures associated to {IFS} with non-uniform contraction ratios

In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, Peres, et al.

2010 Mathematics Subject Classification

Primary 28A15. Secondary 26A30, 26A46, 28A78, 28A80.

Full Text (PDF format)

Published 1 January 2005