From Morse-Smale to all knots and links
From Morse-Smale to all knots and links
复制标题
从 Morse-Smale 到所有结和链节
DOI：
10.1088/0951-7715/11/4/021
复制
发表时间：
1997
期刊：
影响因子：
1.7
通讯作者：
T. Young
中科院分区：
文献类型：
--
作者：
R. Ghrist;T. Young
我们分析了原由Shil'nikov描述的流中部分双曲不动点的某余维一分岔的拓扑（结论）特征。通过修改不变流形缠绕自身的方式，或“褶皱”，我们可以应用模板理论，或分支双流形，来捕获流的拓扑结构。这种分析产生了一类从莫尔斯-小流分岔到包含所有结和连杆类型的周期轨道的小流的流动。
We analyse the topological (knot-theoretic) features of a certain codimension-one bifurcation of a partially hyperbolic fixed point in a flow on originally described by Shil'nikov. By modifying how the invariant manifolds wrap around themselves, or `pleat', we may apply the theory of templates, or branched two-manifolds, to capture the topology of the flow. This analysis yields a class of flows which bifurcate from a Morse-Smale flow to a Smale flow containing periodic orbits of all knot and link types.