Coarse graining: lessons from simple examples

We assess Coarse Graining by studying different partitions of the phase space of the Baker transformation and the periodic torus automorphisms. It turns out that the shape of autocorrelation functions for the Baker transformation is more or less reproduced. However, for certain partitions the decay rates turn out to be irrelevant, even decay may stop in a finite time. For the periodic torus automorphisms, Coarse Graining introduces artificial dumping.