Interférences pour les chats quantiques

In this text I study quantum dynamics of quantized linear automorphisms of the torus after the Ehrenfest time. I show that, in the wave packet basis, the ‘matrix’ of the associated propagator is well approximated by Birkhoff sums of nilrotations on the torus. In the second part, I conduct a thorough study of these sums and relate the equidistribution of evolved wave packets to a problem of Diophantine approximation.