| Full text | |
| Author(s): |
Braun, Francisco
;
Thomaz, Rodrigo
Total Authors: 2
|
| Document type: | Journal article |
| Source: | SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES; v. 19, n. 1, p. 33-pg., 2025-06-01. |
| Abstract | |
Up to topological equivalence, a continuous flow in a surface is determined by its separatrix configuration. This claim is widely known as Markus-Neumann theorem, but it is false with the definition of separatrix originally considered. Recently, Esp & iacute;n Buend & iacute;a and Jim & eacute;nez L & oacute;pez delivered counterexamples and proposed an updated definition of separatrix in order that the claim becomes true. The main objective of this paper is to provide a detailed and self-contained proof of Markus-Neumann theorem taking into account this new definition of separatrices, with a slight generalization. (AU) | |
| FAPESP's process: | 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision |
| Grantee: | Farid Tari |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 23/09684-1 - Topology of polynomial maps through their bifurcation locus |
| Grantee: | Rodrigo Thomaz da Silva |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 21/08895-3 - Qualitative theory of differential equations in the plane: topological classification results |
| Grantee: | Rodrigo Thomaz da Silva |
| Support Opportunities: | Scholarships in Brazil - Master |
| FAPESP's process: | 23/00376-2 - Global injectivity of maps and related topics |
| Grantee: | Francisco Braun |
| Support Opportunities: | Regular Research Grants |