Multifractal formalisms for the local spectral and walk dimensions

B. M. Hambly*, Jun Kigami, Takashi Kumagai

*この研究の対応する著者

研究成果: Article査読

9 被引用数 (Scopus)

抄録

We introduce the concepts of local spectral and walk dimension for fractals. For a class of finitely ramified fractals we show that, if the Laplace operator on the fractal is defined with respect to a multifractal measure, then both the local spectral and walk dimensions will have associated non-trivial multifractal spectra. The multifractal spectra for both dimensions can be calculated and are shown to be transformations of the original underlying multifractal spectrum for the measure, but with respect to the effective resistance metric.

本文言語English
ページ(範囲)555-571
ページ数17
ジャーナルMathematical Proceedings of the Cambridge Philosophical Society
132
3
DOI
出版ステータスPublished - 2002
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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