Decay of correlations for the automorphism of the torus

We present new analytical results concerning Markov partitions, transition matrices and decay of correlations for hyperbolic algebraic automorphisms of the torus . A new numerical tool for the computation of the decay of correlations for automorphism is also illustrated. The tool, based on Markov partitions, allows us to calculate the correlation integrals for a large variety of functions and domains defined in and for a high number of iterations of the map. It can be used to test other numerical and analytical methods for estimating correlation decay.