Weyl asymptotics for Hanoi attractors

2013/07/25 by Patricia Alonso Ruiz, Ruiz, Patricia Alonso, Uta Freiberg +1
Mathematics · Physics and Astronomy · #28A80 #35J05 #35P20 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:28A80 #msc:35J05 #msc:35P20

paper · pdf · doi:10.48550/arxiv.1307.6719

36 pages, corrected typo page 12, updated version with overworked sections 2 and 4

arxiv created 2014/12/23 · arxiv updated 2014/12/24

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.

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