Asymptotic signature of a three-dimensional vector field

被引：12
|
作者：
Gambaudo, JM
Ghys, E
机构：
[1] Univ Bourgogne, Unite Fondamentale Rech Sci & Tech, Lab Topol, CNRS,UMR 5884, F-21078 Dijon, France
[2] Ecole Normale Super Lyon, Unite Math Pures & Appl, CNRS, UMR 5669, F-69364 Lyon 07, France
来源：
DUKE MATHEMATICAL JOURNAL | 2001年 / 106卷 / 01期
关键词：
D O I：
10.1215/S0012-7094-01-10613-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider a volume preserving vector field defined in some compact domain of 3-space and tangent to its boundary. A long piece of orbit can be made into a knot by connecting its endpoints by some arc whose length is less than the diameter of the domain. In this paper, we study the behaviour of the signatures of these knots as the lengths of the pieces of orbits go to infinity. We relate this "asymptotic signature" to the "asymptotic Hopf invariant" that has been studied by Arnold.
引用
收藏
页码：41 / 79
页数：39
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