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

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dc.citation.epage68en_US
dc.citation.issueNumber1en_US
dc.citation.spage43en_US
dc.citation.volumeNumber16en_US
dc.contributor.authorBlasiak, A.en_US
dc.contributor.authorStrichartz, R. S.en_US
dc.contributor.authorUgurcan, B. E.en_US
dc.date.accessioned2016-02-08T10:10:10Z
dc.date.available2016-02-08T10:10:10Z
dc.date.issued2008en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe 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.en_US
dc.identifier.doi10.1142/S0218348X08003818en_US
dc.identifier.eissn1793-6543
dc.identifier.issn0218-348X
dc.identifier.urihttp://hdl.handle.net/11693/23195
dc.language.isoEnglishen_US
dc.publisherWorld Scientific Publishing Co. Pte. Ltd.en_US
dc.relation.isversionofhttp://dx.doi.org/10.1142/S0218348X08003818en_US
dc.source.titleFractalsen_US
dc.subjectLaplacians on fractalsen_US
dc.subjectOuter approximationen_US
dc.subjectSierpinski gasketen_US
dc.subjectSpectrumen_US
dc.subjectApproximation algorithmsen_US
dc.subjectLaplace equationen_US
dc.subjectRecursive functionsen_US
dc.subjectSpectrum analysisen_US
dc.subjectGravitationalen_US
dc.subjectOuter Approximationen_US
dc.subjectTwistsen_US
dc.subjectFractalsen_US
dc.titleSpectra of self-similar Laplacians on the Sierpinski gasket with twistsen_US
dc.typeArticleen_US

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