  We introduce a family of area preserving generalized baker's transformations
acting on the unit square and having sharp polynomial rates of mixing for
Holder data. The construction is geometric, relying on the graph of a single
variable "cut function". Each baker's map B is non-uniformly hyperbolic and
while the exact mixing rate depends on B, all polynomial rates can be attained.
The analysis of mixing rates depends on building a suitable Young tower for an
expanding factor. The mechanisms leading to a slow rate of correlation decay
are especially transparent in our examples due to the simple geometry in the
construction. For this reason we propose this class of maps as an excellent
testing ground for new techniques for the analysis of decay of correlations in
non-uniformly hyperbolic systems. Finally, some of our examples can be seen to
be extensions of certain 1-D non-uniformly expanding maps that have appeared in
the literature over the last twenty years thereby providing a unified treatment
of these interesting and well-studied examples.
