  Chaotic dynamics essentially defines the global properties of gravitating
systems, including, probably, the basics of morphology of galaxies. We use the
Ricci curvature criterion to study the degree of relative chaos (exponential
instability) in core-halo gravitating configurations. We show the existence of
a critical core radius when the system is least chaotic, while systems with
both smaller and larger core radius will typically possess stronger chaotic
properties.
