Topological Entropy and ε-Entropy for Damped Hyperbolic Equations

被引：0

作者：

P. Collet

J.-P. Eckmann

机构：

[1] Centre de Physique Thérique,

[2] UMR 7644,undefined

[3] CNRS,undefined

[4] Ecole Polytechnique,undefined

[5] F-91128 Palaiseau Cedex,undefined

[6] France,undefined

[7] e-mail: collet@cpht.polytechnique.fr,undefined

[8] Département de Physique Théorique and Section de Mathématiques,undefined

[9] Université de Genève,undefined

[10] CH-1211 Genève 4,undefined

[11] Switzerland,undefined

[12] e-mail: eckmann@mykonos.unige.ch,undefined

来源：

Annales Henri Poincaré | 2000年 / 1卷

关键词：

Bounded Domain; Unit Length; Hyperbolic Equation; Topological Entropy; Position Space;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study damped hyperbolic equations on the infinite line. We show that on the global attracting set $ {\cal G} $ the topological entropy per unit length exists in the topology of $ W^{1, \infty} $. We also show that the topological entropy of $ {\cal 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} $.

引用

页码：715 / 752

页数：37