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Multifractal formalisms for the local spectral and walk dimensions

Abstract:

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 w...

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Publication status:
Published

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Publisher copy:
10.1017/S03050041010051618

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Kumagai, T More by this author
Journal:
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
Volume:
132
Issue:
3
Pages:
555-571
Publication date:
2002-05-05
DOI:
EISSN:
1469-8064
ISSN:
0305-0041
URN:
uuid:08f9a0db-0306-4bc4-ae33-4503e0feddb0
Source identifiers:
14366
Local pid:
pubs:14366
Language:
English

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