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Topological equivalence at infinity of a planar vector field and its principal part defined through Newton polytope

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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