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Multifractal structure and product of matrices

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Analysis in Theory and Applications

Abstract

There is a well established multifractal theory for self-similar measures generated by non-overlapping contractive similutudes. Our report here concerns those with overlaps. In particular we restrict our attention to the important classes of self-similar measures that have matrix representations. The dimension spectra and theL q-spectra are analyzed through the product of matrices. There are abnormal behaviors on the multifractal structure and they will be discussed in detail.

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Authors and Affiliations

  1. Department of Mathematics, Chinese University of Hong Kong, Hong Kong

    Lau Ka-sing

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  1. Lau Ka-sing
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Correspondence to Lau Ka-sing.

Additional information

This paper was presented in the Fractal Satellite Conference of ICM 2002 in Nanjing.

The research is supported in part by the HKRGC Grant.

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Ka-sing, L. Multifractal structure and product of matrices. Anal. Theory Appl. 19, 289–311 (2003). https://doi.org/10.1007/BF02835530

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  • DOI: https://doi.org/10.1007/BF02835530

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