EQUIDISTRIBUTION GF EIGENVALUES AND SEMIC LASSICAL ERGODICITY OF QUANTIZED SYMPLECTOMORPHISMS OF THE TORUS

We show that the eigenvalues (quasi-energies) of the quantized hyperbo lic automorphisms of the torus and of their quantized smooth Hamiltoni an perturbations are semiclassically equidistributed on the unit circl e. As a corollary we obtain the equipartition of the eigenfunctions co rresponding to quasi-energies confined to an arc of the quasi-energy c ercle. (C) Academie des Sciences/Elsevier, Paris.