| Full text | |
| Author(s): |
Braun, Francisco
;
Fernandes, Filipe
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 320, p. 10-pg., 2022-05-25. |
| Abstract | |
Denote by r(n) the maximal number of Reeb components that a nonsingular polynomial differential system of degree non the real plane can have. It is known that r(0) = r(1) = 0, r(2) = r(3) = 2and n - 1 <= r(n) <= n for n >= 4. In this paper we prove that r(n) = nfor all n = 4. This completely solves, for nonsingular systems, a problem posed by Chicone and Tian in 1982. We prove our result by explicitly constructing nonsingular Hamiltonian systems of degree npresenting nReeb components for any n >= 4. (C) 2022 Elsevier Inc. All rights reserved. (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: | 20/14498-4 - Global injectivity of maps and related topics |
| Grantee: | Francisco Braun |
| Support Opportunities: | Regular Research Grants |