  This paper summarises a numerical investigation of how the usual
manifestations of chaos and regularity for flows in time-independent
Hamiltonians can be alterred by a systematic time-dependence of the form
arising naturally in an expanding Universe. If the time-dependence is not too
strong, the observed behaviour can be understood in an adiabatic approximation.
One still infers sharp distinctions between regular and chaotic behaviour, even
though ``regular'' does not mean ``periodic'' and ``chaotic'' will not in
general imply strictly exponential sensitivity towards small changes in initial
conditions. However, these distinctions are no longer absolute, as it is
possible for a single orbit to change from regular to chaotic and/or visa
versa. If the time-dependence becomes too strong, the distinction between
regular and chaotic can disappear so that no sensitive dependence on initial
conditions is manifest.
