  Properties related to entanglement in quantum systems, are known to be
associated with distinct properties of the corresponding classical systems, as
for example stability, integrability and chaos. This means that the detailed
topology, both local and global, of the classical phase space may reveal, or
influence, the entangling power of the quantum system. As it has been shown in
the literature, the bifurcation points, in autonomous dynamical systems, play a
crucial role for the onset of entanglement. Similarly, the existence of scars
among the quantum states seems to be a factor in the dynamics of entanglement.
Here we study these issues for a non-autonomous system, the Quantum Kicked Top,
as a collective model of a multi-qubit system. Using the bifurcation diagram of
the corresponding classical limit (the Classical Kicked Top), we analyzed the
pair-wise and the bi-partite entanglement of the qubits and their relation to
scars, as a function of the critical parameter of the system. We found that the
pair-wise entanglement and pair-wise negativity show a strong maximum precisely
at the bifurcation points, while the bi-partite entanglement changes slope at
these points. We have also investigated the connection between entanglement and
the fixed points on the branch of the bifurcation diagram between the two first
bifurcation points and we found that the entanglement measures take their
extreme values precisely on these points. We conjecture that our results on
this behaviour of entanglement is generic for many quantum systems with a
non-linear classical analogue.
