  We consider simulations of a 2-dimensional gas of hard disks in a rectangular
container and study the Lyapunov spectrum near the vanishing Lyapunov
exponents. To this spectrum are associated ``eigen-directions'', called
Lyapunov modes. We carefully analyze these modes and show how they are
naturally associated with vector fields over the container. We also show that
the Lyapunov exponents, and the coupled dynamics of the modes (where it exists)
follow linear laws, whose coefficients only depend on the density of the gas,
but not on aspect ratio and very little on the boundary conditions.
