On the dynamics of generators of Cauchy horizons

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.