  We clarify some points about the systems considered by Sota, Suzuki and Maeda
in Class. Quantum Grav. 13, 1241 (1996). Contrary to the authors' claim for a
non-homoclinic kind of chaos, we show the chaotic cases they considered are
homoclinic in origin. The power of local criteria to predict chaos is once more
questioned. We find that their local, curvature--based criterion is neither
necessary nor sufficient for the occurrence of chaos. In fact, we argue that a
merit of their search for local criteria applied to General Relativity is just
to stress the weakness of locality itself, free of any pathologies related to
the motion in effective Riemannian geometries.
