| Full text | |
| Author(s): |
Braun, Francisco
;
Meza-Sarmiento, Ingrid S.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 521, n. 2, p. 25-pg., 2022-12-20. |
| Abstract | |
Let f, g : R2 -> R be two submersion functions and o(f) and o(g) be the regular foliations of R2 whose leaves are the connected components of the levels sets of f and g, respectively. The topological equivalence of f and g implies the topological equivalence of o(f) and o(g), but the converse is not true, in general. In this paper, we introduce the class of linear-like submersion functions, which is wide enough in order to contain non-trivial behaviors, and provide conditions for the validity of the converse implication for functions inside this class. Our results lead us to a complete topological invariant for topological equivalence in a certain subclass of linear-like submersion functions. (c) 2022 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 20/14498-4 - Global injectivity of maps and related topics |
| Grantee: | Francisco Braun |
| Support Opportunities: | Regular Research Grants |
| 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 |