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Experimental Mathematics Volume 31, 2022 - Issue 3
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Original Articles

Spectral Properties of Laplacians on Snowflake Domains and Filled Julia Sets

Robert S. Strichartza Department of Mathematics, Cornell University, Ithaca, NY, USAView further author information
&
Samuel C. Wieseb Department of Mathematics, Universität Leipzig, Leipzig, GermanyCorrespondence[email protected]
View further author information
Pages 1014-1025 | Published online: 26 Mar 2020
 
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Abstract

We present eigenvalue data and pictures of eigenfunctions of the classic and quadratic snowflake fractal and of quadratic filled Julia sets. Furthermore, we approximate the area and box-counting dimension of selected Julia sets to compare the eigenvalue counting function with the Weyl term.

2000 Mathematics Subject Classification:

Declaration of Interest

No potential conflict of interest was reported by the author(s).

Additional information

Funding

SCW was supported by the Foundation of German Business (SDW).

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