24 citations · 36 across the 10 of their papers we have counts for
12 papers
Bifurcation of limit cycles in piecewise holomorphic systems separated by two external circles
Carlos Vinícius das Neves Silva, Paulo Ricardo da Silva
This work investigates the number of limit cycles bifurcating from the periodic orbits of a linear center when it is perturbed by piecewise holomorphic systems with three zones sep…
Simultaneous bifurcation of limit cycles for Piecewise Holomorphic systems
Armengol Gasull, Gabriel Rondón, Paulo R. da Silva
Let be a holomorphic differential equation with center at . In this paper we are concerned about studying the piecewise perturbation systems $\dot{z}=f(z)+εR^\pm(…
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…
On the number of limit cycles for piecewise polynomial holomorphic systems
Armengol Gasull, Gabriel Rondón, Paulo R. da Silva
In this paper we are concerned with determining lower bounds of the number of limit cycles for piecewise polynomial holomorphic systems with a straight line of discontinuity. We ap…
Holomorphic slow-fast systems
Gabriel Rondón, Paulo R. da Silva, Luiz F. S. Gouveia
In this paper, we are concerned with studying the existence of invariant complex manifolds of two-dimensional holomorphic systems. From the geometric singular perturbation theory w…
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 Planar Holomorphic Systems
L. F. S. Gouveia, G. Rondón, P. R. da Silva
Planar holomorphic systems , are those that and for some holomorphic function . They have i…
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…
Phase Portrait of the Riccati Quadratic Polynomial Differential Systems
Jaume Llibre, Bruno Dominiciano Lopes, Paulo Ricardo da Silva
In this paper we characterize the phase portrait of the Riccati quadratic polynomial differential systems with $(x,y)\in…
Slow--fast systems and sliding on codimension 2 switching manifolds
Paulo Ricardo da Silva, Willian Pereira Nunes
In this work we consider piecewise smooth vector fields defined in , where is a self-intersecting switching manifold. A double regularization of is a 2…
Nonlinear Sliding of Discontinuous Vector Fields and Singular Perturbation
Paulo Ricardo da Silva, Ingrid Sofia Meza-Sarmiento, Douglas Duarte Novaes
We consider piecewise smooth vector fields (PSVF) defined in open sets with switching manifold being a smooth surface . The PSVF are given by pairs $X = (X_+, X…
Canard Cycles and Poincaré Index of Non-Smooth Vector Fields on the Plane
Claudio Buzzi, Tiago de Carvalho, Paulo Ricardo da Silva
This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for t…