  We study the dynamical properties of the Dicke model for increasing spin
length, as the system approaches the limit of a classical spin. First, we
describe the emergence of collective excitations above the groundstate that
converge to the coupled spin-oscillator oscillations found in the classical
limit. The corresponding Green functions reveal quantum dynamical signatures
close to the superradiant quantum phase transition. Second, we identify
signatures of classical quasi-periodic orbits in the quantum time evolution
using numerical time-propagation of the wave function. The resulting phase
space plots are compared to the classical trajectories. We complete our study
with the analysis of individual eigenstates close to the quasi-periodic orbits.
