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
SN - 0305-0041
VL - 132
SP - 555
EP - 571
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 3
ER -