Overview

The simplest examples of chaotic Hamiltonian systems are the Anosov automorphisms of the 2d torus. Their quantization therefore yields a class of systems where questions of quantum chaos can be addressed with relative The simplest examples of chaotic Hamiltonian systems are the Anosov automorphisms of the 2d torus. Their quantization therefore yields a class of systems where questions of quantum chaos can be addressed with relative ease. In these lectures I will present and prove some recent results on the phenomenon of "scarring" of eigenstates of the quantized maps by the unstable periodic orbits of the Anosov automorphisms. The lectures are based on joint work with F. Bonechi, F. Faure and S. Nonnenmacher, and the corresponding papers can be found on my website http://www-gat.univ-lille1.fr/~debievre/