  Using the Schwarz function of an ellipse, it was recently shown that galaxies
with density constant on confocal ellipses can produce at most four ``bright''
images of a single source. The more physically interesting example of an
isothermal galaxy has density that is constant on \emph{homothetic} ellipses.
In that case bright images can be seen to correspond to zeros of a certain
transcendental harmonic mapping. We use complex dynamics to give an upper bound
on the total number of such zeros.
