Multifractal formalisms for the local spectral and walk dimensions

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)555-571
Number of pages17
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
Publication statusPublished - 2002
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)


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