Polynomial decay of correlations for almost Anosov diffeomorphisms

Abstract

We investigate the polynomial lower and upper bounds for decay of correlations of a class of two-dimensional almost Anosov diffeomorphisms with respect to their Sinai–Ruelle–Bowen (SRB) measures. The degrees of the bounds are determined by the expansion and contraction rates as the orbits approach the indifferent fixed point, and are expressed by using coefficients of the third-order terms in the Taylor expansions of the diffeomorphisms at the indifferent fixed point.