Chaos in Hamiltonians with a Cosmological Time Dependence

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.