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.
Original language | English |
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Pages (from-to) | 227-244 |
Number of pages | 18 |
Journal | Asian Journal of Mathematics |
Volume | 9 |
Issue number | 2 |
DOIs | |
State | Published - 2005 |
Scopus Subject Areas
- General Mathematics
- Applied Mathematics
Keywords
- Absolute continuity
- Iterated function system
- Self-similar measure
- Transversality condition