Geodesic
Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet
Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 153-180

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DOI

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 Sierpinski carpets. For all these functions the leading term is of the form $ {{x}^{\text{ }\!\!\gamma\!\!\text{ }}}\phi \left( \log x \right)$ for a suitable exponent $\text{ }\!\!\gamma\!\!\text{ }$ and $\phi $ a periodic function. We also discuss similar results for the heat content of affine nested fractals.
DOI : 10.4153/CJM-2010-079-7
Mots-clés : 35K05, 28A80, 35B40, 60J65 
Hambly, B. M. Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet. Canadian journal of mathematics, Tome 63 (2011) no. 1, pp. 153-180. doi: 10.4153/CJM-2010-079-7
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     title = {Asymptotics for {Functions} {Associated} with {Heat} {Flow} on the {Sierpinski} {Carpet}},
     journal = {Canadian journal of mathematics},
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     year = {2011},
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     doi = {10.4153/CJM-2010-079-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-079-7/}
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