Abstract
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.
Citation
Sze-Man Ngai. Yang Wang. "Self-similar measures associated to {IFS} with non-uniform contraction ratios." Asian J. Math. 9 (2) 227 - 244, June 2005.
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