English

Vibration Spectra of the $m$-Tree Fractal

Classical Analysis and ODEs 2011-05-11 v1 Spectral Theory

Abstract

We introduce a family of post-critically finite fractal trees indexed by the number of branches they possess. Then we produce a Laplacian operator on graph approximations to these fractals and use spectral decimation to describe the spectrum of the Laplacian on these trees. Lastly we consider the behavior of the spectrum as the number of branches increases.

Keywords

Cite

@article{arxiv.0812.2867,
  title  = {Vibration Spectra of the $m$-Tree Fractal},
  author = {Daniel Ford and Benjamin Steinhurst},
  journal= {arXiv preprint arXiv:0812.2867},
  year   = {2011}
}

Comments

21 pages, 4 figures