Singularity and L2-Dimension of Self-Similar Measures

Sze Man Ngai

doi:10.1016/j.chaos.2011.12.010

Singularity and L²-Dimension of Self-Similar Measures

Sze Man Ngai

Mathematical Sciences

Hunan Normal University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	American English
Journal	Chaos, Solitons & Fractals
Volume	45
DOIs	https://doi.org/10.1016/j.chaos.2011.12.010
State	Published - Jan 1 2012

Keywords

L2-dimension

DC Disciplines

Education
Mathematics

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10.1016/j.chaos.2011.12.010License: Unspecified

http://dx.doi.org/10.1016/j.chaos.2011.12.010

Cite this

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AB - 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.

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