Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet

http://dx.doi.org/10.4153/CJM-2010-079-7
Canad. J. Math. 63(2011), 153-180

  Published:2010-11-06
 Printed: Feb 2011

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 $x^{\gamma}\phi(\log x)$ for a suitable exponent $\gamma$ and $\phi$ a periodic function. We also discuss similar results for the heat content of affine nested fractals.