Spectral asymptotics for Stretched Fractals
Spectral Theory
2018-09-28 v1
Abstract
The Stretched Sierpinski Gasket (or Hanoi attractor) was subject of several prior works. In this work we use this idea of stretching self-similar sets to obtain non-self-similar ones. We are able to do this for a subset of the connected p.c.f. self-similar sets that fulfill a certain connectivity condition. We construct Dirichlet forms and study the associated self-adjoint operators by calculating the Hausdorff dimension w.r.t. the resistance metric as well as the leading term of the eigenvalue counting function.
Keywords
Cite
@article{arxiv.1809.10367,
title = {Spectral asymptotics for Stretched Fractals},
author = {Elias Hauser},
journal= {arXiv preprint arXiv:1809.10367},
year = {2018}
}