On the Markus-Neumann theorem
On the Markus-Neumann theorem
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关于马库斯-诺依曼定理
DOI：
10.1016/j.jde.2018.07.021
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
V'ictor Jim'enez Lop'ez
中科院分区：
文献类型：
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作者：
J. G. E. Buend'ia;V'ictor Jim'enez Lop'ez
L. Markus [6]，后来由D.A. Neumann [7]推广，指出曲面上的两个连续流是等价的当且仅当存在一个曲面同胚保持它们的分界线配置的轨道和时间方向.本文给出几个例子，表明Markus-Neumann定理不需要工作，因为最初的表述.此外，我们指出了它的证明中的差距，并展示了如何以一种正确的（稍微更一般的）方式重述它。
A well-known result by L. Markus [6], later extended by D.A. Neumann [7], states that two continuous flows on a surface are equivalent if and only if there is a surface homeomorphism preserving orbits and time directions of their separatrix configurations.In this paper we present several examples showing that, as originally formulated, the Markus–Neumann theorem needs not work. Besides, we point out the gap in its proof and show how to restate it in a correct (and slightly more general) way.