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arXiv · 1707.05504

On the Markus-Neumann theorem

José Ginés Espín Buendía·Víctor Jiménez Lopéz
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Abstract

A well-known result by L. Markus, later extended by D. A. Neumann, 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.

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José Ginés Espín Buendía, Víctor Jiménez Lopéz. 2017-07-18. On the Markus-Neumann theorem. https://arxiv.org/abs/1707.05504

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