Analysis on the Projective Octagasket

DOI10.1142/9789811215537_0009zbMATH Open1453.28011arXiv1801.07758OpenAlexW3200854354MaRDI QIDQ5137256

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

Publication date: 2 December 2020

Published in: Analysis, Probability and Mathematical Physics on Fractals (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1801.07758

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Fractals (28A80)