P. Collet, J.-P. Eckmann
Topological Entropy and epsilon-Entropy
for Damped Hyperbolic Equations
(361K, pstscript)
ABSTRACT. 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 $W^{1,\infty}$.