Topological Entropy and epsilon-Entropy for Damped Hyperbolic Equations

Abstract

We study damped hyperbolic equations on the infinite line. We show that on the global attracting set $G$ the $ε$-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 $W^{1,\infty}$.