Spectral asymptotics for Stretched Fractals

Elias Hauser

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arXiv · 1809.10367

Spectral asymptotics for Stretched Fractals

Elias Hauser

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Abstract

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.

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BibTeX RIS

Elias Hauser. 2018-09-27. Spectral asymptotics for Stretched Fractals. https://arxiv.org/abs/1809.10367

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