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

Sze Man Ngai, Yang Wang

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

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 languageEnglish
Pages (from-to)227-244
Number of pages18
JournalAsian Journal of Mathematics
Volume9
Issue number2
DOIs
StatePublished - 2005

Scopus Subject Areas

  • General Mathematics
  • Applied Mathematics

Keywords

  • Absolute continuity
  • Iterated function system
  • Self-similar measure
  • Transversality condition

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