  This work results from our attempts to solve Boltzmann-Sinai's hypothesis
about the ergodicity of hard ball gases. A crucial element in the studies of
the dynamics of hard balls is the analysis of special hypersurfaces in the
phase space consisting of degenerate trajectories (which lack complete
hyperbolicity). We prove that if a flow-invariant hypersurface $J$ in the phase
space of a semi-dispersing billiard has a negative Lyapunov function, then the
volume of the forward image of $J$ grows at least linearly in time. Our proof
is independent of the solution of the Boltzmann-Sinai hypothesis, and we
provide a complete and self-contained argument here.
