Smoothing continuous flows on two-manifolds and recurrences
Smoothing continuous flows on two-manifolds and recurrences
复制标题
平滑两个流形上的连续流和递归
DOI：
10.1017/s0143385700003278
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发表时间：
1986
影响因子：
0.9
通讯作者：
C. Gutierrez
中科院分区：
文献类型：
--
作者：
C. Gutierrez
设φ：φ × M → M是紧致C∞双流形M上的连续流。证明了M上存在一个与φ拓扑等价的C1流，并且证明了下列条件是等价的：（a）φ的任意极小集是平凡的;（B）φ拓扑等价于一个C2流;（c）φ拓扑等价于一个C∞流.证明了具有非平凡常返性的连续流的结构和存在定理。
Abstract Let φ: ℝ × M → M be a continuous flow on a compact C∞ two-manifold M. It is proved that there exists a C1 flow ψ on M which is topologically equivalent to φ, and that the following conditions are equivalent: (a) any minimal set of φ is trivial; (b) φ is topologically equivalent to a C2 flow; (c) φ is topologically equivalent to a C∞ flow. Also proved is a structure and an existence theorem for continuous flows with non-trivial recurrence.