Spectral asymptotics on the Hanoi attractor

2017/10/17 by Elias Hauser, Hauser, Elias
Mathematics · #FOS: Mathematics #Spectral Theory (math.SP) #math.SP

paper · pdf · doi:10.48550/arxiv.1710.06204

arxiv created 2018/07/23 · arxiv updated 2018/07/24

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.

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