Estimates of correlation decay in auto/endomorphisms of the \(n\)-torus (Q5948851)

The authors study three classes of mappings of the \(n\)-dimensional torus generated by linear mappings with matrices \(M\): hyperbolic automorphisms, endomorphisms with hyperbolic \(M\) (assuming that the spectrum of \(M\) has parts both outside and inside the unit disk), and purely expanding automorphisms. They obtain exponential and superexponential estimates of autocorrelation decay for smooth and analytic observables.