Pseudo–symmetries of anosov maps and spectral statistics, Nonlinearity 13(3

Abstract. The statistics of the quantum eigenvalues of certain families of nonlinear maps on the 2-torus are found not to belong to the universality classes one would expect from the symmetries of the (classical) dynamics the maps generate. These anomalies are shown to be caused by arithmetical quantum symmetries which do not have a classical limit. They are related to the dynamics generated by associated linear torus maps on particular rational lattices that form the support of the quantum Wigner functions. (Some figures in this article appear in black and white in the printed version.