Journal article

### Finitely ramified graph-directed fractals, spectral asymptotics and the multidimensional renewal theorem

Abstract:

We consider the class of graph-directed constructions which are connected and have the property of finite ramification. By assuming the existence of a fixed point for a certain renormalization map, it is possible to construct a Laplace operator on fractals in this class via their Dirichlet forms. Our main aim is to consider the eigenvalues of the Laplace operator and provide a formula for the spectral dimension, the exponent determining the power-law scaling in the eigenvalue counting functio...

Publication status:
Published

### Access Document

Publisher copy:
10.1017/S0013091500000730

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
Volume:
46
Issue:
1
Pages:
1-34
Publication date:
2003-02-01
DOI:
EISSN:
1464-3839
ISSN:
0013-0915
Source identifiers:
3431
Language:
English
Keywords:
Pubs id:
pubs:3431
UUID:
uuid:fbcbdfb5-3d5b-4ac2-8797-4ab8983ac2bc
Local pid:
pubs:3431
Deposit date:
2012-12-19