论文标题
由莫尔斯 - 男性梯度样流动引起的稳定叶子和CW结构
Stable foliations and CW-structure induced by a Morse-Smale gradient-like flow
论文作者
论文摘要
我们证明，封闭的歧管上的摩尔斯 - 摩尔梯度状流动具有“兼容不变稳定叶子的系统”，该系统类似于Palis和Smale引入的对象，证明了Morse-Smale-Smale-Male-Smale-Smale-Male-Male-Smale diffefyomorphismismiss和Frows的结构稳定性，但具有确定的正常和几何性能。我们展示了如何使用这些不变的叶子来给出一个独立的证明，证明了众所周知但相当微妙的定理表明，在封闭的歧管上，类似莫尔斯 - 男性梯度流的不稳定流形是$ cw $ $ m $ $ m $ $ m $的开放单元。
We prove that a Morse-Smale gradient-like flow on a closed manifold has a "system of compatible invariant stable foliations" that is analogous to the object introduced by Palis and Smale in their proof of the structural stability of Morse-Smale diffeomorphisms and flows, but with finer regularity and geometric properties. We show how these invariant foliations can be used in order to give a self-contained proof of the well-known but quite delicate theorem stating that the unstable manifolds of a Morse-Smale gradient-like flow on a closed manifold $M$ are the open cells of a $CW$-decomposition of $M$.
