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Topological Entropy and epsilon-Entropy for Damped Hyperbolic Equations

Pierre Collet·Jean-Pierre Eckmann
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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 $W^{1,\infty}$.

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Pierre Collet, Jean-Pierre Eckmann. 1999-08-16. Topological Entropy and epsilon-Entropy for Damped Hyperbolic Equations. https://doi.org/10.1007/pl00001013

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