沿流程平滑切换
Smooth shifts along flows
摘要：
设$Φ$是光滑紧致有限维流形$M$上的流。考虑$C^{\infty}(M,M)$的子集$E(Φ)$和$D(Φ)$，它们分别由$M$的光滑映射和保流$Φ$的叶状的双同态组成。还令$E_{0}(Φ)$和$D_{0}(Φ)$是具有紧开拓扑的$E(Φ)$和$D(Φ)$的身份路径分量。证明了在$Φ$的不动点上，在适当的条件下，包含$D_{0}(Φ) \subset E_{0}(Φ)$是一个同伦等价，并且这些空间与圆是可缩的或同伦等价的.
英文摘要：
Let $Φ$ be a flow on a smooth, compact, finite-dimensional manifold $M$. Consider the subsets $E(Φ)$ and $D(Φ)$ of $C^{\infty}(M,M)$ consisting of smoothh mappings and diffeomorphisms (respectively) of $M$ preserving the foliation of the flow $Φ$. Let also $E_{0}(Φ)$ and $D_{0}(Φ)$ be the identity path components of $E(Φ)$ and $D(Φ)$ with compact-open topology. We prove that under mild conditions on fixed points of $Φ$ the inclusion $D_{0}(Φ) \subset E_{0}(Φ)$ is a homotopy equivalence and these spaces are either contractible or homotopically equivalent to the circle.
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