  We discuss various features of the dynamical system determined by the flow of
null geodesic generators of Cauchy horizons. Several examples with non--trivial
(``chaotic'', ``strange attractors'', etc.) global behaviour are constructed.
Those examples are relevant to the ``chronology protection conjecture'', and
they show that the occurrence of ``fountains'' is {\em not} a generic feature
of Cauchy horizons.
