Analysis on the Projective Octagasket
Spectral Theory
2018-01-25 v1
Abstract
The existence of a self similar Laplacian on the Projective Octagasket, a non-finitely ramified fractal is only conjectured. We present experimental results using a cell approximation technique originally given by Kusuoka and Zhou. A rigorous recursive algorithm for the discrete Laplacian is given. Further, the spectrum and eigenfunctions of the Laplacian together with its symmetries are categorized and utilized in the construction of solutions to the heat equation.
Keywords
Cite
@article{arxiv.1801.07758,
title = {Analysis on the Projective Octagasket},
author = {Yiran Mao and Robert S. Strichartz and Levente Szabo and Wing Hong Wong},
journal= {arXiv preprint arXiv:1801.07758},
year = {2018}
}