  We present a complete analysis of the dynamics of a Bose-Einstein condensate
trapped in a symmetric triple-well potential. Our classical analogue treatment,
based on a time-dependent variational method using SU(3) coherent states,
includes the parameter dependence analysis of the equilibrium points and their
local stability, which is closely related to the condensate collective
behaviour. We also consider the effects of off-site interactions, and how these
"cross-collisions" may become relevant for a large number of trapped bosons.
Besides, we have shown analytically, by means of a simple basis transformation
in the single-particle space, that an integrable sub-regime, known as
twin-condensate dynamics, corresponds in the classical phase space to invariant
surfaces isomorphic to the unit sphere. However, the quantum dynamics preserves
the twin-condensate defining characteristics only partially, thus breaking the
invariance of the associated quantum subspace. Moreover, the periodic geometry
of the trapping potential allowed us to investigate the dynamics of finite
angular momentum collective excitations, which can be suppressed by the
emergence of chaos. Finally, using the generalized purity associated to the
su(3) algebra, we were able to quantify the dynamical classicality of a quantum
evolved system, as compared to the corresponding classical trajectory.
