  In this paper we exhibit new classes of smooth systems which satisfy the
Central Limit Theorem (CLT) and have (at least) one of the following
properties:
  (1) zero entropy;
  (2) weak but not strong mixing;
  (3) (polynomially) mixing but not $K$;
  (4) $K$ but not Bernoulli;
  (5) non Bernoulli and mixing at arbitrary fast polynomial rate.
  We also give an example of a system satisfying the CLT where the normalizing
sequence is regularly varying with index $1$.
