Multifractal formalisms for the local spectral and walk dimensions
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-tri...
| Hoofdauteurs: | , , |
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| Formaat: | Journal article |
| Taal: | English |
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2002
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| _version_ | 1826258120366620672 |
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| author | Hambly, B Kigami, J Kumagai, T |
| author_facet | Hambly, B Kigami, J Kumagai, T |
| author_sort | Hambly, B |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T18:29:00Z |
| format | Journal article |
| id | oxford-uuid:08f9a0db-0306-4bc4-ae33-4503e0feddb0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:29:00Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:08f9a0db-0306-4bc4-ae33-4503e0feddb02022-03-26T09:15:49ZMultifractal formalisms for the local spectral and walk dimensionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:08f9a0db-0306-4bc4-ae33-4503e0feddb0EnglishSymplectic Elements at Oxford2002Hambly, BKigami, JKumagai, TWe 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. |
| spellingShingle | Hambly, B Kigami, J Kumagai, T Multifractal formalisms for the local spectral and walk dimensions |
| title | Multifractal formalisms for the local spectral and walk dimensions |
| title_full | Multifractal formalisms for the local spectral and walk dimensions |
| title_fullStr | Multifractal formalisms for the local spectral and walk dimensions |
| title_full_unstemmed | Multifractal formalisms for the local spectral and walk dimensions |
| title_short | Multifractal formalisms for the local spectral and walk dimensions |
| title_sort | multifractal formalisms for the local spectral and walk dimensions |
| work_keys_str_mv | AT hamblyb multifractalformalismsforthelocalspectralandwalkdimensions AT kigamij multifractalformalismsforthelocalspectralandwalkdimensions AT kumagait multifractalformalismsforthelocalspectralandwalkdimensions |