Prequantum transfer operator for symplectic Anosov diffeomorphism

The authors define the prequantization of a symplectic and Anosov diffeomorphism. They study the spectral properties of the transfer operator associated to a smooth potential. After restriction to the $N$-th Fourier mode and letting $N$ tend to infinity, a structure of concentric bands appear. They study the eigenvalue repartition in the most external band and they show that this repartition follows a Weyl law. The authors give a physical interpretation of the results and they compare them to the geometric quantization which appears in quantum chaos theory.