Analysis on the Projective Octagasket

Yiran Mao; Robert S. Strichartz; Levente Szabo; Wing Hong Wong

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arXiv · 1801.07758

Analysis on the Projective Octagasket

Yiran Mao·Robert S. Strichartz·Levente Szabo·Wing Hong Wong

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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.

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BibTeX RIS

Yiran Mao, Robert S. Strichartz, Levente Szabo, Wing Hong Wong. 2018-01-23. Analysis on the Projective Octagasket. https://arxiv.org/abs/1801.07758

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