  We examine the dynamics of subsystems of bipartite and tripartite quantum
systems with nonlinear Hamiltonians. We consider two models which capture the
generic features of open quantum systems: a three-level atom interacting with a
single-mode radiation field, and a three-level atom interacting with two field
modes which do not directly interact with each other. The entanglement of
specific initially unentangled states of the atom-field system is examined
through the time-varying subsystem von Neumann entropy (SVNE). The counterparts
of near-revivals and fractional revivals of the initial state are clearly
identifiable in the SVNE in all cases where revival phenomena occur. The Mandel
$Q$ parameter corresponding to the photon number of a radiation field is
obtained as a function of time in both models. In those cases where revivals
are absent, a time series analysis of the mean photon number reveals a variety
of ergodicity properties (as manifested in return maps, recurrence-time
distributions and Lyapunov exponents), depending on the strength of the
nonlinearity and the degree of coherence of the initial state of the radiation
field(s).
