  High resolution eigenvalue spectra of several two- and three-dimensional
superconducting microwave cavities have been measured in the frequency range
below 20 GHz and analyzed using a statistical measure which is given by the
distribution of the normalized mode fluctuations. For chaotic systems the limit
distribution is conjectured to show a universal Gaussian, whereas integrable
systems should exhibit a non-Gaussian limit distribution. For the investigated
Bunimovich stadium and the 3D-Sinai billiard we find that the distribution is
in good agreement with this prediction. We study members of the family of
limacon billiards, having mixed dynamics. It turns out that in this case the
number of approximately 1000 eigenvalues for each billiard does not allow to
observe significant deviations from a Gaussian, whereas an also measured
circular billiard with regular dynamics shows the expected difference from a
Gaussian.
