Self-Similar Measures Associated to {IFS} with Non-Uniform Contraction Ratios

Authors

Sze-Man Ngai, Georgia Southern UniversityFollow
Yang Wang, Georgia Institute of TechnologyFollow

Document Type

Article

Publication Date

6-2005

Publication Title

The Asian Journal of Mathematics

DOI

10.4310/AJM.2005.v9.n2.a7

ISSN

1945-0036

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.

Comments

© 2005 International Press of Boston. This is an open access article retrieved from the Asian Journal of Mathematics. Articles older than 5 years are open access.

Recommended Citation

Ngai, Sze-Man, Yang Wang. 2005. "Self-Similar Measures Associated to {IFS} with Non-Uniform Contraction Ratios." The Asian Journal of Mathematics, 9 (2): 227-244. doi: 10.4310/AJM.2005.v9.n2.a7
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/603