F.Bonechi, S.De Bievre
Controlling strong scarring for quantized ergodic toral automorphisms
(58K, Latex)

ABSTRACT.  We show that in the semi-classical limit the eigenfunctions 
of quantized ergodic symplectic toral automorphisms can not concentrate 
in measure on a finite number of closed orbits of the dynamics. More 
generally, we show that, if the pure point component of the limit 
measure has support on a finite number of such orbits, then the mass 
of this component 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.