Weyl asymptotics for Hanoi attractors

TL;DR

This paper investigates the eigenvalue distribution of Laplacians on Hanoi attractors, a class of fractals, by developing new methods to handle their non self-similar structure.

Contribution

It introduces a modified construction of Laplacians on non self-similar fractals, combining discrete and quantum graph techniques.

Findings

Eigenvalue counting function asymptotics determined

Dirichlet and resistance forms constructed

Method adapted for non self-similar fractals

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.