  We study individual eigenstates of quantized area-preserving maps on the
2-torus which are classically chaotic. In order to analyze their semiclassical
behavior, we use the Bargmann-Husimi representations for quantum states, as
well as their stellar parametrization, which encodes states through a minimal
set of points in phase space (the constellation of zeros of the Husimi
density). We rigorously prove that a semiclassical uniform distribution of
Husimi densities on the torus entails a similar equidistribution for the
corresponding constellations. We deduce from this property a universal behavior
for the phase patterns of chaotic Bargmann eigenfunctions, which reminds of the
WKB approximation for eigenstates of integrable systems (though in a weaker
sense). In order to obtain more precise information on ``chaotic
eigenconstellations", we then model their properties by ensembles of random
states, generalizing former results on the 2-sphere to the torus geometry. This
approach yields statistical predictions for the constellations, which fit quite
well the chaotic data. We finally observe that specific dynamical information,
e.g. the presence of high peaks (like scars) in Husimi densities, can be
recovered from the knowledge of a few long-wavelength Fourier coefficients,
which therefore appear as valuable order parameters at the level of individual
chaotic eigenfunctions.
