Cláudio Gomes Pessoa

• Abstract

  In this project, our goal is to study isochronous centers on central manifolds of polynomial vector fields in R3. We will develop mathematical methods that allow the characterization of these centers according to the parameters of the system, avoiding, if possible, the direct restriction of the vector field to the finite expansion of a center manifold. Once characterized, we will focus on…

  Isochronous Centers on Center Manifolds, AP.R

• Abstract

  The theory of dynamical systems is one of the most important tools in the qualitative and quantitative study of mathematical models of applied sciences. Most of these models are formulated using differential equations (continuous dynamic systems). Since the first works published by Poincaré at the end of the 19th century, the qualitative theory of differential equations has experienced a …

  Continuous or piecewise smooth dynamical systems on 2 and 3 dimensional manifolds., AP.R
• Advances in Qualitative Theory of Differential Equations 2023, AR.EXT

(Only some records are available in English at this moment)

• Abstract

  In this project our goal is the study of monodrome nilpotent singular points in center manifolds of vector fields in R3. We will look for a result that characterizes these points according to the parameters of the system and without the necessity of restricting it to a center manifold. Once characterized, we will focus on finding techniques to solve the center-focus problem for these sing…

  Nilpotent centers on the center manifolds, BP.DR

• Abstract

  The theory of dynamical systems is one of the most important tools in quantitative and qualitative study of mathematical models of applied sciences. Most of these models are formulated using differential equations (continuous dynamical systems). Since the first published work by Poincaré in the late nineteenth century, the qualitative theory of differential equations have experienced a si…

  Fundamentals of the Qualitative Theory of Differential Equations, BP.IC

• Abstract

  A teoria dos sistemas dinâmicos é uma das ferramentas mais importantes no estudo qualitativo e quantitativo dos modelos matemáticos de ciências aplicadas. A maioria destes modelos são formulados usando-se equações diferenciais (sistemas dinâmicos contínuos). Desde os primeiros trabalhos publicados por Poincaré no final do século XIX, a teoria qualitativa das equações diferenciais tem expe…

  Campos de vetores polinomiais homogeneos na esfera de dimensao 2., BP.PD

(Only some records are available in English at this moment)

• Abstract

  This project contemplates the study of the time of the solution curves for differential equations when distinct types of bifurcations occur, focusing in three topics: the study of the period of limit-cycles generated by non-elementary bifurcations, the time delay associated to the bottleneck or ghost phenomenom and the improvement of tools to obtain uniform developments of the period func…

  Bifurcation phenomena in time of differential equations, BE.EP.DR

• Abstract

  In this project our goal is the study of some current problems of the Qualitative Theory of the Ordinary Differentials Equations. We will study the Center-Focus Problem in central manifolds of vector fields in R3 and the Dulac's Problem for monodromic singular points of piecewise analytic vector fields in the plane.We will develop a method that allows us to computate the Lyapunov coeffici…

  Dulac's Problem and of the Focus Center on Two-Dimensional Manifolds, BE.PQ