  The three-disk scatterer has served as a paradigm for semiclassical periodic
orbit quantization of classical chaotic systems using Gutzwiller's trace
formula. It represents an open quantum system, thus leading to spectra of
complex eigenenergies. An interesting general feature of open quantum systems
described by non-Hermitian operators is the possible existence of exceptional
points where not only the complex eigenvalues but also their respective
eigenvectors coincide. Using Gutzwiller's periodic orbit theory we show that
exceptional points exist in a three-disk scatterer if the system's geometry is
modified by extending the system from circular to elliptical disks. The
extension is implemented in such a way that the system's characteristic
$C_{3\mathrm{v}}$ symmetry is preserved. The two-dimensional parameter plane of
the system is then spanned by the distance between and the excentricity of the
elliptical disks. As typical signatures of exceptional points we observe the
permutation of two resonances when an exceptional point is encircled in
parameter space, and a non-Lorentzian resonance line shape in the weighted
density of states.
