Weyl asymptotics for Hanoi attractors
Spectral Theory
2014-12-24 v4 Mathematical Physics
math.MP
Abstract
The asymptotic behaviour of the eigenvalue counting function of Laplacians on Hanoi attractors is determined. To this end, Dirichlet and resistance forms are constructed. Due to the non self-similarity of these sets, the classical construction of the Laplacian for p.c.f. self-similar fractals has to be modified by combining discrete and quantum graphs methods.
Cite
@article{arxiv.1307.6719,
title = {Weyl asymptotics for Hanoi attractors},
author = {Patricia Alonso Ruiz and Uta Freiberg},
journal= {arXiv preprint arXiv:1307.6719},
year = {2014}
}
Comments
36 pages, corrected typo page 12, updated version with overworked sections 2 and 4