阻尼双曲型方程的拓扑熵和ε-熵
Topological Entropy and epsilon-Entropy for Damped Hyperbolic Equations
摘要：
研究无限长直线上的阻尼双曲型方程。证明了在全局吸引集$G$上，$W^{1,\infty}$拓扑中存在$ε$ -熵（单位长度）.我们还证明了$G$的单位长度拓扑熵是存在的。这些结果显示使用两个主要的技术：在有界域的位置空间和大动量，和一个新的submultiplicativity参数$W^{1,\infty}$。
英文摘要：
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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