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Universidade de São Paulo - ICMC/USP
Universidade de São Paulo - ICMC/USP
Topological equivalence at infinity of some planar vector fields and its principal part via Newton polytope
Topological equivalence at infinity of some planar vector fields and its principal part via Newton polytope
Resumo: Let X be a planar polynomial vector field with a fixed Newton polytope Γ. Recently, in Dalbelo-Oliveira-Perez (2024), it was proved that the monomials associated to the upper boundary of Γ satisfying some non-degeneracy conditions determine, under topological equivalence, the phase portrait of X in a neighbourhood of the boundary of the Poincaré–Lyapunov disc.
In the present talk we show that there exist vector fields of chief interest which do not satisfy such non-degeneracy conditions but still their phase portraits are determined by the monomials associated to the upper boundary of Γ in the Newton polytope of X and using such a result we can complete classify locally some classes of planar vector fields at infinity in the Poincaré-Lyapunov disc.
Data: 18/02
Data: 18/02
Horário: 17h00
Horário: 17h00
Local: Bloco F67 (Dep. de Matemática) da UEM
Local: Bloco F67 (Dep. de Matemática) da UEM
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