  In this paper we study decay of correlations and limit theorems for
generalized baker's transformations. Our examples are piecewise non-uniformly
hyperbolic maps on the unit square that posses two spatially separated lines of
indifferent fixed points.
  We obtain sharp rates of mixing for Lipschitz functions on the unit square
and limit theorems for H\"older observables on the unit square. Some of our
limit theorems exhibit convergence to non-normal stable distributions for
H\"older observables. We observe that stable distributions with any skewness
parameter in the allowable range of $[-1,1]$ can be obtained as a limit and
derive an explicit relationship between the skewness parameter and the values
of the H\"older observable along the lines of indifferent fixed points.
  This paper is the first application of anisotropic Banach space methods and
operator renewal theory to generalized baker's transformations. Our decay of
correlations results recover the results of Bose and Murray. Our results on
limit theorems are new for generalized baker's transformations.
