  In this work we obtain mixing (and in some cases sharp mixing rates) for a
reasonable large class of invertible systems preserving an infinite measure.
The examples considered here are the invertible analogue of both Markov and non
Markov unit interval maps. Moreover, we obtain results on the decay of
correlation in the finite case of invertible non Markov maps, which, to our
knowledge, were not previously addressed.
  The present method consists of a combination of the framework of operator
renewal theory, as introduced in the context of dynamical systems by Sarig
[39], with the framework of function spaces of distributions developed in the
recent years along the lines of Blank, Keller and Liverani [9].
