  The Lyapunov spectrum corresponding to a periodic orbit for a two dimensional
many particle system with hard core interactions is discussed. Noting that the
matrix to describe the tangent space dynamics has the block cyclic structure,
the calculation of the Lyapunov spectrum is attributed to the eigenvalue
problem of a 16x16 reduced matrices regardless of the number of particles. We
show that there is the thermodynamic limit of the Lyapunov spectrum in this
periodic orbit. The Lyapunov spectrum has a step structure, which is explained
by using symmetries of the reduced matrices.
