Abstract. L.S. Young's 1998 tower construction provided exponential
decay of correlations for Holder functions for 2-D hyperbolic
systems with singularies and as a consequence a CLT, for instance.
Our interest is to develop further the probabilistic methods, 
in particular, those based on the Fourier-transform of the Perron-
Frobenius operator in order to obtain more delicate probabilistic
properties. The methods are also hoped to lead to a potential theory
of 2-D periodic Lorentz processes.