The Arnold cat map, the Ulam method and time reversal

► The Ulam method is used to study dynamical and statistical properties of the Arnold cat map. ► The properties of eigenvalues and eigenvectors of the Ulam matrix approximant are determined. ► Their relations to the Fokker-Planck relaxation and the Kolmogorov-Sinai entropy are established. ► The Ulam time scale for time reversal is shown to depend logarithmically on the matrix size.