  We explore the dynamical stability of the minisuperspace Hamiltonian of the
Bianchi IX cosmological models, giving a gauge-invariant and unapproximated
description of the full continuous dynamics, achieved through a geometrical
description of the equations of motion in the framework of the theory of
Finsler Spaces. The numerical integrations of the geodesics and geodesic
deviation equations show clearly the absence of any "traditional" signature of
Chaos, while suggesting a chaotic scattering dynamics scenario.
