  We outline the covariant nature of the chaos characterizing the generic
cosmological solution near the initial singularity. Our analysis is based on a
"gauge" independent ADM-reduction of the dynamics to the physical degrees of
freedom, and shows that the dynamics is isomorphic point by point in space to a
billiard on a Lobachevsky plane. The Jacobi metric associated to the geodesic
flow is constructed and a non-zero Lyapunov exponent is explicitly calculated.
The chaos covariance emerges from the independence of the form of the lapse
function and the shift vector.
