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Zbl 1041.28006
Strichartz, Robert S.
Fractafolds based on the Sierpiński gasket and their spectra. (English)
[J] Trans. Am. Math. Soc. 355, No. 10, 4019-4043 (2003). ISSN 0002-9947; ISSN 1088-6850/e

In the paper the author starts from the Sierpiński gasket fractal and defines the fractafold. It is shown that any fractafold based on the Sierpiński gasket fractal has a cellular construction and it is shown explicitly how to obtain the spectrum of the fractafold from the spectrum of the graph, using the spectral decimation method. It is also shown that although the Sierpiński gasket fractal is topologically rigid, there are fractafolds that are not topologically rigid.
[Nicolae-Adrian Secelean (Sibiu)]

MSC 2000:: *28A80 Fractals
37C70 Attractors and repellers, topological structure

Keywords: fractafold; fractal; Sierpiński gasket; iterated function system; topological rigidity; spectral decimation

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