DECAY OF CORRELATIONS FOR CERTAIN MULTIDIMENSIONAL MAPS

We study the decay of correlations for certain multi-dimensional nonin vertible maps which do not necessarily satisfy Renyi's condition (the bounded distortion property) and do not necessarily satisfy the Markov condition on the definite partitions. Our method is based on the tech nique of Markov approximations which was developed by Chernov. We rela te the slowness of the; decay of correlations to the singularity of th e invariant density which is caused by the lack of hyperbolicity. We a lso see that it can be described by the distortion property of the dis tributions of the invariant densities.