| Full text | |
| Author(s): |
Dalbelo, Thais Maria
;
Oliveira, Regilene
;
Perez, Otavio Henrique
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 408, p. 24-pg., 2024-07-08. |
| Abstract | |
Given a planar polynomial vector field X with a fixed Newton polytope P , we prove (under some non-degeneracy conditions) that the monomials associated to the upper boundary of P determine (under topological equivalence) the phase portrait of X in a neighborhood of boundary of the Poincar & eacute;-Lyapunov disk. This result can be seen as a version of the well known result of Berezovskaya, Brunella and Miari [2,5] for the dynamics at infinity. We also discuss the non-existence of periodic orbits near infinity via Newton polytope, as well as the effect of the Poincar & eacute;-Lyapunov compactification on P . (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| FAPESP's process: | 19/21181-0 - New frontiers in Singularity Theory |
| Grantee: | Regilene Delazari dos Santos Oliveira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 21/10198-9 - Invariant manifolds and limit periodic sets of discontinuous foliations |
| Grantee: | Otavio Henrique Perez |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 23/01018-2 - Determinantal varieties, Euler obstruction, and Whitney equisingularity |
| Grantee: | Thais Maria Dalbelo |
| Support Opportunities: | Scholarships abroad - Research |