Estimates of correlation decay in auto/endomorphisms of the n-Torus

Abstract We apply spectral methods to estimate the correlation decay of smooth and analytic observables for the algebraic automorphisms and endomorphisms of the n -torus, under conditions of hyperbolicity or pure expansivity. The exponential and superexponential estimates achieved generalize and improve analogous results already known about this subject and may provide useful reliability tests for the numerical calculation of correlations of more general maps.