TY - JOUR

T1 - Multifractal formalisms for the local spectral and walk dimensions

AU - Hambly, B. M.

AU - Kigami, Jun

AU - Kumagai, Takashi

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

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U2 - 10.1017/S0305004101005618

DO - 10.1017/S0305004101005618

M3 - Article

AN - SCOPUS:0036339363

VL - 132

SP - 555

EP - 571

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -