We show that in the semiclassical limit the eigenfunctions of
quantized ergodic symplectic toral automorphisms cannot concentrate in
measure on closed orbits of the dynamics. More generally, we show that
the mass of the pure point component of the limit measure must be
smaller than two thirds of the total mass. The proofs use only the
algebraic (i.e., not the number-theoretic) properties of the toral
automorphisms together with the exponential instability of the
dynamics and therefore work in all dimensions.