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Self-Similar Measures Associated To {Ifs} With Non-Uniform Contraction Ratios, Sze-Man Ngai, Yang Wang
Self-Similar Measures Associated To {Ifs} With Non-Uniform Contraction Ratios, Sze-Man Ngai, Yang Wang
Department of Mathematical Sciences Faculty Publications
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.