Spectra of self-similar Laplacians on the Sierpinski gasket with twists
Author
Blasiak, A.
Strichartz, R. S.
Ugurcan, B. E.
Date
2008Source Title
Fractals
Print ISSN
0218-348X
Electronic ISSN
1793-6543
Publisher
World Scientific Publishing Co. Pte. Ltd.
Volume
16
Issue
1
Pages
43 - 68
Language
English
Type
ArticleItem Usage Stats
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Abstract
We study the spectra of a two-parameter family of self-similar Laplacians on the Sierpinski gasket (SG) with twists. By this we mean that instead of the usual IFS that yields SG as its invariant set, we compose each mapping with a reflection to obtain a new IFS that still has SG as its invariant set, but changes the definition of self-similarity. Using recent results of Cucuringu and Strichartz, we are able to approximate the spectra of these Laplacians by two different methods. To each Laplacian we associate a self-similar embedding of SG into the plane, and we present experimental evidence that the method of outer approximation, recently introduced by Berry, Goff and Strichartz, when applied to this embedding, yields the spectrum of the Laplacian (up to a constant multiple). © 2008 World Scientific Publishing Company.
Keywords
Laplacians on fractalsOuter approximation
Sierpinski gasket
Spectrum
Approximation algorithms
Laplace equation
Recursive functions
Spectrum analysis
Gravitational
Outer Approximation
Twists
Fractals