 0281 F.Bonechi, S.De Bievre
 Controlling strong scarring for quantized ergodic toral automorphisms
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Feb 21, 02

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Abstract. We show that in the semiclassical 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.
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