Spectral asymptotics on the Hanoi attractor

TL;DR

This paper investigates the spectral properties of the Hanoi attractor, a non-self-similar fractal with symmetry, by calculating the leading asymptotic term of the eigenvalue counting function for associated operators.

Contribution

It provides the first explicit calculation of the eigenvalue asymptotics for operators defined on the Hanoi attractor, extending spectral analysis to non-self-similar fractals.

Findings

Derived the leading asymptotic term for eigenvalue counting functions

Extended spectral analysis techniques to non-self-similar fractals

Confirmed the existence of symmetric resistance forms on the Hanoi attractor

Abstract

The Hanoi attractor (or Stretched Sierpinski Gasket) is an example of a non-self-similar fractal that still exhibits a lot of symmetry. The existence of various symmetric resistance forms on the Hanoi attractor was shown in 2016 by Alonso-Ruiz, Freiberg and Kigami. To get self adjoint operators from these resistance forms we have to choose a locally finite measure. The goal of this paper is to calculate the leading term for the asymptotics of the eigenvalue counting function from these operators.