Topological Entropy and epsilon-Entropy for Damped Hyperbolic Equations

Details Topological Entropy and epsilon-Entropy for Damped Hyperbolic Equations Topological Entropy and epsilon-Entropy for Damped Hyperbolic Equations

1999-08-16

arxiv.org/abs/math/9908080v1

Mathematics

Dynamical Systems

38 pages, no figures, plain.tex

Scientific paper

10.1007/PL00001013

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 $W^{1,\infty}$.

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