Spectral asymptotics for Stretched Fractals

The Stretched Sierpinski Gasket (or Hanoi attractor) was subject of several prior works. In this work we use this idea of stretching self-similar sets to obtain non-self-similar ones. We are able to do this for a subset of the connected p.c.f. self-similar sets that fulfill a certain connectivity co...

Full description

Saved in:
Bibliographic Details
Main Author Hauser, Elias
Format Journal Article
LanguageEnglish
Published 27.09.2018
Subjects
Mathematics - Spectral Theory
Online AccessGet full text
DOI10.48550/arxiv.1809.10367

Cover

More Information
Summary:The Stretched Sierpinski Gasket (or Hanoi attractor) was subject of several prior works. In this work we use this idea of stretching self-similar sets to obtain non-self-similar ones. We are able to do this for a subset of the connected p.c.f. self-similar sets that fulfill a certain connectivity condition. We construct Dirichlet forms and study the associated self-adjoint operators by calculating the Hausdorff dimension w.r.t. the resistance metric as well as the leading term of the eigenvalue counting function.
DOI:10.48550/arxiv.1809.10367