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fractal graphs

Proceedings of the Edinburgh Mathematical Society (1)

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The spectra of the Laplacians of fractal graphs not satisfying spectral decimation
Part of
- Classical measure theory
Jonathan Jordan
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 3 / October 2010

Published online by Cambridge University Press:

12 August 2010, pp. 731-746
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We consider the spectra of the Laplacians of two sequences of fractal graphs in the context of the general theory introduced by Sabot in 2003. For the sequence of graphs associated with the pentagasket, we give a description of the eigenvalues in terms of the iteration of a map from (ℂ2)3 to itself. For the sequence of graphs introduced in a previous paper by the author, we show that the results found therein can be related to Sabot's theory.