Singularity and L²-Dimension of Self-Similar Measures

Authors

Sze-Man Ngai, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

2012

Publication Title

Chaos, Solitons & Fractals

DOI

10.1016/j.chaos.2011.12.010

Abstract

We study self-similar measures defined by non-uniformly contractive iterated function systems of similitudes with overlaps. In the case the contraction ratios of the similitudes are exponentially commensurable, we describe a method to compute the L²-dimension of the associated self-similar measures. Our result allows us to determine the singularity of some of such measures.

Recommended Citation

Ngai, Sze-Man. 2012. "Singularity and L²-Dimension of Self-Similar Measures." Chaos, Solitons & Fractals, 45 (3): 256-265. doi: 10.1016/j.chaos.2011.12.010
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/128