A characterization of self-similar measures

Shuicao Zheng and Huonan Lin

Chaos, Solitons & Fractals, 2007, vol. 34, issue 5, 1613-1621

Abstract: For a graph directed self-similar set, we investigate a list of invariant self-similar measures. In particular, the existence of the local dimension of the associated self-similar measure is determined. Consequently, the multifractal decomposition of the graph directed self-similar set can be formulated under the open set condition. This give a positive answer to a question posed by Edgar and Mauldin, as well as Olsen.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:34:y:2007:i:5:p:1613-1621

DOI: 10.1016/j.chaos.2006.04.063

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