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      Spectra of self-similar Laplacians on the Sierpinski gasket with twists

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      Author
      Blasiak, A.
      Strichartz, R. S.
      Ugurcan, B. E.
      Date
      2008
      Source 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
      Article
      Item 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 fractals
      Outer approximation
      Sierpinski gasket
      Spectrum
      Approximation algorithms
      Laplace equation
      Recursive functions
      Spectrum analysis
      Gravitational
      Outer Approximation
      Twists
      Fractals
      Permalink
      http://hdl.handle.net/11693/23195
      Published Version (Please cite this version)
      http://dx.doi.org/10.1142/S0218348X08003818
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      • Department of Mathematics 635
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