| We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional smooth hard disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by the computation of the full set of covariant perturbation vectors co-moving with the flow in tangent-space. These vectors are shown to be transversal but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The mode-supporting degenerate subspaces are dynamically isolated, and the Oseledec splitting is uniformly dominated. Some results for rough disks are also shown. |
|