Journal article

### 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...

Publication status:
Published

### Access Document

Publisher copy:
10.1017/S03050041010051618

### Authors

More by this author
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