Dimension of homogeneous rational self-similar measures with overlaps (Q1014699)
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scientific article; zbMATH DE number 5549434
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| English | Dimension of homogeneous rational self-similar measures with overlaps |
scientific article; zbMATH DE number 5549434 |
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Dimension of homogeneous rational self-similar measures with overlaps (English)
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29 April 2009
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The self-similar measures play an important role in the studies of fractal geometry, the case having overlaps is still a difficult question. The author consider a class of self-similar measures with overlaps which are obtained from systems of homotheties with centres in a lattice where the contraction ratios are all equal to the inverse of a natural number \(L\). In this case, the author gets the local dimension of the measure as the Shannon entropy (up to a constant), which shows also some relations with the properties of the absolute continuity or singularity of the measure.
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self-similar measures
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overlapping
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dimension
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Shannon entropy
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ergodicity
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hidden Markov chain
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