On the Markus-Neumann theorem
Dynamical Systems
2017-07-19 v1
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.
Keywords
Cite
@article{arxiv.1707.05504,
title = {On the Markus-Neumann theorem},
author = {José Ginés Espín Buendía and Víctor Jiménez Lopéz},
journal= {arXiv preprint arXiv:1707.05504},
year = {2017}
}
Comments
14 pages, 4 figures