Subexponential decay of correlations

We describe a method for proving subexponential lower bounds for correlations functions, and apply it to study decay of correlations for maps with countable Markov partitions. One result is that LS Young’s upper estimates Y2] are optimal in many situations. Our method is based on a general result concerning the asymptotics of renewal sequences of bounded operators acting on Banach spaces, which we apply to the iterates of the transfer operator. Oblatum 14-VII-2001 & 5-VI-2002?Published online: 6 August 2002 Dedicated to B. Weiss on the occasion of his 60th birthday RID="*" ID="*"This research was supported by the Nuffield Foundation, NUF-NAL 00.