- 02-81 F.Bonechi, S.De Bievre
- Controlling strong scarring for quantized ergodic toral automorphisms
Feb 21, 02
(auto. generated ps),
of related papers
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.