7 papers
Generalized upper principal part of real planar polynomial vector fields
Thaís Maria Dalbelo, Regilene Oliveira, Otavio Henrique Perez
The goal of this paper is to generalize recent results about the topological classification of the dynamics of a real planar polynomial vector field near infinity. Given a polynomi…
Polynomial slow-fast systems on the Poincaré-Lyapunov sphere
Otavio Henrique Perez, Paulo Ricardo da Silva
The main goal of this paper is to study compactifications of polynomial slow-fast systems. More precisely, the aim is to give conditions in order to guarantee normal hyperbolicity…
Topological equivalence in the infinity of a planar vector field and its principal part defined through Newton polytope
Thais Maria Dalbelo, Regilene Oliveira, Otavio Henrique Perez
Given a planar polynomial vector field with a fixed Newton polytope , we prove (under some non degeneracy conditions) that the monomials associated to the upper bo…
Slow-fast normal forms arising from piecewise smooth vector fields
Otavio Henrique Perez, Gabriel Rondón, Paulo Ricardo da Silva
We studied piecewise smooth differential systems of the form where $F: \ma…
On the classification of planar constrained differential systems under topological equivalence
Otavio Henrique Perez, Paulo Ricardo da Silva
This paper concerns the local study of analytic constrained differential systems (or impasse systems) of the form , , where is a vector…
Resolution of singularities of 2-dimensional real analytic constrained differential systems
Otavio Henrique Perez, Paulo Ricardo da Silva
We present a theorem of resolution of singularities for real analytic constrained differential systems defined on a 2-manifold with corners having impasse set…