Spectral asymptotics 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.