  We study damped hyperbolic equations on the infinite line. We show that on
the global attracting set $G$ the $\epsilon$-entropy (per unit length) exists
in the topology of $W^{1,\infty}$. We also show that the topological entropy
per unit length of $G$ exists. These results are shown using two main
techniques: Bounds in bounded domains in position space and for large momenta,
and a novel submultiplicativity argument in $W^{1,\infty}$.
