  We demonstrate the existence and significance of diffractive orbits in an
open microwave billiard, both experimentally and theoretically. Orbits that
diffract off of a sharp edge strongly influence the conduction spectrum of this
resonator, especially in the regime where there are no stable classical orbits.
On resonance, the wavefunctions are influenced by both classical and
diffractive orbits. Off resonance, the wavefunctions are determined by the
constructive interference of multiple transient, nonperiodic orbits.
Experimental, numerical, and semiclassical results are presented.
