  We study the quantum-classical correspondence for systems with interacting
spin-particles that are strongly chaotic in the classical limit. This is done
in the presence of constants of motion associated with the fixed angular
momenta of individual spins. Our analysis of the Lyapunov spectra reveals that
the largest Lyapunov exponent agrees with the Lyapunov exponent that determines
the local instability of each individual spin moving under the influence of all
other spins. Within this picture, we introduce a rigorous and simple test of
ergodicity for the spin motion, and use it to identify when classical chaos is
both strong and global in phase space. In the quantum domain, our analysis of
the Hamiltonian matrix in a proper representation allows us to obtain the
conditions for the onset of quantum chaos as a function of the model
parameters. From the comparison between the quantum and classical domains, we
demonstrate that quantum quantities, such as the local density of states (LDOS)
and the shape of the chaotic eigenfunctions written in the non-interacting
many-body basis, have well-defined classical counterparts. Another central
finding is the relationship between the Kolmogorov-Sinai entropy and the width
of the LDOS, which is useful for studies of many-body dynamics.
