Realisation of an directed equipped bipartite graph by an Omega-stable flow on a closed surface

Title Realisation of an directed equipped bipartite graph by an Omega-stable flow on a closed surface V. E. Kruglov1, 2, O. V. Pochinka11National Research University Higher School of Economics 2Lobachevsky State University A lot of many sorts of graphs (directed, multicolored, bipartite, etc.) were repeatedly used to describe and realize systems with regular dynamics on surfaces. For example, Morse-Smale flows are completely described by a directed graph equipped with a subgraph system. In addition, their dynamics can be described by three-color graphs. Four-color graphs describe the dynamics of some non structurally unstable vector fields, and a directed bipartite graph, equipped with additional information, is a complete topological invariant for $\Omega$-stable flows. In this paper, for each oriented equipped bipartite graph, we construct a standard $\Omega$-stable flow on a closed surface. realisation, $\Omega$-stable flow, equipped graph Kruglov V. E., Pochinka O. V. ''Realisation of an directed equipped bipartite graph by an Omega-stable flow on a closed surface'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 418-427. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper59.pdf. - Date of access: 24.06.2019.