Can you hear the fractal dimension of a drum

@article{Arrighetti2005CanYH,
  title={Can you hear the fractal dimension of a drum},
  author={W. Arrighetti and G. Gerosa},
  journal={arXiv: Spectral Theory},
  year={2005}
}
Electromagnetics and Acoustics on a bounded domain are governed by the Helmholtz's equation; when such a domain is a [pre-]fractal described by means of a `just-touching' Iterated Function System (IFS) spectral decomposition of the Helmholtz's operator is self-similar as well. Renormalization of the Green's function proves this feature and isolates a subclass of eigenmodes, called ``diaperiodic'', whose waveforms and eigenvalues can be recursively computed applying the IFS to the initiator's… Expand
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Can One Hear the Shape of a Drum