Knots and Orbit Genealogies in Three Dimensional Flows
Knots and Orbit Genealogies in Three Dimensional Flows
复制标题
三维流动中的结和轨道谱系
DOI：
10.1007/978-94-015-8238-4_4
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
P. Holmes
中科院分区：
文献类型：
--
作者：
R. Ghrist;P. Holmes
本文综述了应用纽结和链环理论研究三维流动周期轨道结构的方法和结果。特别是，我们研究的家谱周期轨道的“自然”暂停的马蹄形R 2。通过沿沿着强稳定流形折叠，我们得到了模板，一个分支的两个流形携带一个半流，它保留了原始流的纽结和链接数据。与额外的工具的一维揉捏理论和哈密顿分歧理论，我们表明如何有关马蹄结的结果可以用来研究分歧的两个参数家庭的Henon映射。
We present a survey of methods and results in the application of knot and link theory to the study of periodic orbit structures in three dimensional flows. In particular, we examine the genealogy of periodic orbits in the “natural” suspension of the horseshoe diffeomorphism on R 2. By collapsing along strong stable manifolds, we obtain the template, a branched two-manifold carrying a semiflow which preserves the knot and link data of the original flow. With the additional tools of one-dimensional kneading theory and Hamiltonian bifurcation theory, we indicate how results concerning horseshoe knots can be used to study bifurcations in a two-parameter family of Henon maps.