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Resonance spectra of two-dimensional dielectric microwave resonators ofcircular and square shapes have been measured. The deduced length spectra ofperiodic orbits were analyzed and a trace formula for dielectric resonatorsrecently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] wastested. The observed deviations between the experimental length spectra and thepredictions of the trace formula are attributed to a large number of missingresonances in the measured spectra. We show that by taking into account thesystematics of observed and missing resonances the experimental length spectraare fully understood. In particular, a connection between the most long-livedresonances and certain periodic orbits is established experimentally.

Experimental test of a trace formula for two-dimensional dielectric resonators