Abstract
In this paper we give an example of a nonlattice self-similar fractal string such that the set of real parts of their complex dimensions has an isolated point. This proves that, in general, the set of dimensions of fractality of a fractal string is not a perfect set.
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References
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Lapidus, M.L., Van Frankenhuysen, M.: Fractal geometry, complex dimensions and zeta functions: geometry and spectra of fractal strings. Springer monographs in mathematics. 2nd edn. Springer, New York (2013)
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Mora, G., Sepulcre, J.M. & Vidal, T. On the existence of fractal strings whose set of dimensions of fractality is not perfect. RACSAM 109, 11–14 (2015). https://doi.org/10.1007/s13398-014-0164-8
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DOI: https://doi.org/10.1007/s13398-014-0164-8