2017/07/18 by José Ginés Espín Buendía, Buendía, José Ginés Espín, Vı́ctor Jiménez López +1
Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.1707.05504
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.