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 with respect to the effective resistance metric. © 2002 Cambridge Philosophical Society.

Publication status:: Published

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APA Style

Hambly, B., Kigami, J., & Kumagai, T. (2002). Multifractal formalisms for the local spectral and walk dimensions. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 132(3), 555–571.

MLA Style

Hambly, B., et al. “Multifractal Formalisms for the Local Spectral and Walk Dimensions.” MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, vol. 132, no. 3, 2002, pp. 555–71.

Chicago Style

Hambly, B, J Kigami, and T Kumagai. 2002. “Multifractal Formalisms for the Local Spectral and Walk Dimensions.” MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY 132 (3): 555–71.
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Publisher copy:: 10.1017/S03050041010051618

Authors

+ Hambly, B More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Kigami, J More by this author

Role:: Author

+ Kumagai, T More by this author

Role:: Author

Journal:: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY More from this journal
Volume:: 132
Issue:: 3
Pages:: 555-571
Publication date:: 2002-05-01
DOI:: 10.1017/S03050041010051618
EISSN:: 1469-8064
ISSN:: 0305-0041

Language:: English
Pubs id:: pubs:14366
UUID:: uuid:08f9a0db-0306-4bc4-ae33-4503e0feddb0
Local pid:: pubs:14366
Source identifiers:: 14366
Deposit date:: 2012-12-19

Terms of use

Copyright date:: 2002

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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