Autor(es)

Dalbelo, Thais Maria ; Oliveira, Regilene ; Perez, Otavio Henrique

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 408, p. 24-pg., 2024-07-08.

Resumo

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)

• Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
• Beneficiário: Regilene Delazari dos Santos Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 21/10198-9 - Variedades invariantes e conjuntos periódicos limite de folheações descontínuas
• Beneficiário: Otavio Henrique Perez
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 23/01018-2 - Variedades determinantais, obstrução de Euler e equisingularidade de Whitney
• Beneficiário: Thais Maria Dalbelo
• Modalidade de apoio: Bolsas no Exterior - Pesquisa