  In this paper we present a new approach for studying the dynamics of
spatially inhomogeneous cosmological models with one spatial degree of freedom.
By introducing suitable scale-invariant dependent variables we write the
evolution equations of the Einstein field equations as a system of autonomous
partial differential equations in first-order symmetric hyperbolic format,
whose explicit form depends on the choice of gauge. As a first application, we
show that the asymptotic behaviour near the cosmological initial singularity
can be given a simple geometrical description in terms of the local past
attractor on the boundary of the scale-invariant dynamical state space. The
analysis suggests the name ``asymptotic silence'' to describe the evolution of
the gravitational field near the cosmological initial singularity.
