8 papers
On the topological invariance of the algebraic multiplicity of holomorphic foliations
Leonardo M. Câmara, Fernando Reis, José Edson Sampaio
In this paper, we address one of the most basic and fundamental problems in the theory of foliations and ODEs, the topological invariance of the algebraic multiplicity of a holomor…
On flags of holomorphic foliations associated with singular second-order ordinary differential equations
Fernando Lourenço, Eurípedes da Silva, Fernando Reis
We consider germs of holomorphic vector fields at the origin of , with non-isolated singularities that are tangent to a holomorphic foliation of codimension one. This…
Topology of first integrals via Milnor fibrations II
Fernando Reis, Maico Ribeiro, Euripedes da Silva
This survey is the continuation of a series of works aimed at applying tools from Singularity Theory to Differential Equations. More precisely, we utilize the powerfull Milnor's Fi…
A brief introduction on residue theory of holomorphic foliations
Fernando Lourenço, Fernando Reis
This is a survey paper dealing with holomorphic foliations, with emphasis on residue theory and its applications. We start recalling the definition of holomorphic foliations as a s…
Instantons and transseries of the Mathieu potential deformed by a -symmetry parameter
N. M. Alvarenga, E. Cavalcanti, C. A. Linhares +3
We investigate the non-perturbative effects of a deformation of the Mathieu differential equation consistent with symmetry. First, we develop a connection between th…
Energy levels for -symmetric deformation of the Mathieu equation
E. Cavalcanti, N. M. Alvarenga, F. Reis +3
We propose a non-Hermitian deformation of the Mathieu equation that preserves symmetry and study its spectrum and the transition from -unbroken to $\ma…
On the integrability of Hill's equation of the motion of the moon
Fernando Reis, Bruno Scárdua
We study under the standpoint of integrable complex analytic 1-forms (complex analytic foliations), a class of second order ordinary differential equations with periodic coefficien…
On first integrals admitting asymptotic expansion for holomorphic foliations in dimension two
F. Reis
In this paper we study the dynamics of a holomorphic vector field near a singular point in dimension two using asymptotic expansion techniques. We consider a holomorphic vector fie…