  We consider classical two-dimensional Kepler system with spin-orbit coupling
and show that at a sufficiently strong coupling it demonstrates a chaotic
behavior. The chaos emerges since the spin-orbit coupling reduces the number of
the integrals of motion as compared to the number of the degrees of freedom.
This reduction is manifested in the equations of motion as the emergence of the
anomalous velocity determined by the spin orientation. By using analytical and
numerical arguments, we demonstrate that the chaotic behavior, being driven by
this anomalous term, is related to the system energy dependence on the initial
spin orientation. We observe the critical dependence of the dynamics on the
initial conditions, where system can enter and exit a stability domain by very
small changes in the initial spin orientation. Thus, this system can
demonstrate a reentrant order-from-disorder transition driven by very small
variations in the initial conditions.
