Mathematical Sciences: Faculty Publications
Iterated Function Systems with Overlaps and Self-Similar Measures
Document Type
Article
Publication Date
2-2001
Publication Title
Journal of London Mathematical Society
DOI
10.1112/S0024610700001654
ISSN
1469-7750
Abstract
The paper considers the iterated function systems of similitudes which satisfy a separation condition weaker than the open set condition, in that it allows overlaps in the iteration. Such systems include the well-known Bernoulli convolutions associated with the PV numbers, and the contractive similitudes associated with integral matrices. The latter appears frequently in wavelet analysis and the theory of tilings. One of the basic questions is studied: the absolute continuity and singularity of the self-similar measures generated by such systems. Various conditions to determine the dichotomy are given.
Recommended Citation
Lau, Ka-Sing, Sze-Man Ngai, Hui Rao.
2001.
"Iterated Function Systems with Overlaps and Self-Similar Measures."
Journal of London Mathematical Society, 63 (1): 99-116.
doi: 10.1112/S0024610700001654
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/607
Copyright
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