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A characterization of self-similar measures

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  • Zheng, Shuicao
  • Lin, Huonan

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.

Suggested Citation

  • Zheng, Shuicao & Lin, Huonan, 2007. "A characterization of self-similar measures," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1613-1621.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1613-1621
    DOI: 10.1016/j.chaos.2006.04.063
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    References listed on IDEAS

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    1. Li, Yueling & Dai, Chaoshou, 2006. "A multifractal formalism in a probability space," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 57-73.
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