- Abstract:
- We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpiñski carpets. For all these functions the leading term is of the form xγφ(log x) for a suitable exponent γ and φ a periodic function. We also discuss similar results for the heat content of affine nested fractals. © Canadian Mathematical Society 2010.
- Publication status:
- Published
- Publisher copy:
- 10.4153/CJM-2010-079-7
-
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- Journal:
- CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
- Volume:
- 63
- Issue:
- 1
- Pages:
- 153-180
- Publication date:
- 2011-02-05
- DOI:
- EISSN:
-
1496-4279
- ISSN:
-
0008-414X
- URN:
-
uuid:c8f8e615-b551-4273-bf06-68158c5a6c7d
- Source identifiers:
-
120299
- Local pid:
- pubs:120299
- Language:
- English
- Copyright date:
- 2011
Journal article
Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet
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