Spectral Properties of Laplacians on Snowflake domains and filled Julia sets

Spectral Properties of Laplacians on Snowflake domains and filled Julia sets

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.

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Veröffentlicht in:arXiv.org 2019-03
Hauptverfasser: Strichartz, Robert S, Wiese, Samuel C
Format: Artikel
Sprache:eng
Schlagworte:
Domains
Eigenvalues
Eigenvectors
Pictures
Snowflakes
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Beschreibung
Zusammenfassung: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.
ISSN:2331-8422