CV Lattes
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Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. Instituto de Biociências, Letras e Ciências Exatas (IBILCE) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduate at Licenciatura Em Matemática from Universidade Estadual Paulista Júlio de Mesquita Filho (1992), master's at Mathematics from Universidade Estadual de Campinas (1995) and ph.d. at Mathematics from Universidade Estadual de Campinas (1999). Has experience in Mathematics, focusing on Dynamic Systems, acting on the following subjects: sistemas dinâmicos, sistemas reversíveis, teoria qualitativa, equações diferenciais ordinárias and sistemas hamiltonianos. (Source: Lattes Curriculum)
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We will study problems related to the existence, nonexistence, and bifurcation of isolated periodic orbits (limit cycles) in planar piecewise polynomial systems. The first problem is the extension of Bendixson Dulac's theory in piecewise differential systems defined in two zones. The second is the simultaneous bifurcation of limit cycles near piecewise Hamiltonian centers with more than o…
This project is a continuation of the thematic project: Ergodic and Qualitative Theories of Dynamical Systems (process 2013 / 24541-0). Our goal is to study several problems in the area of dynamical systems and their connections with other areas such as Analysis, Ergodic Theory, Number Theory, Topology among many others. The problems to be addressed are current and include the following t…
We will study the isolated periodic orbits (limit cycles) in planar piecewise polynomial systems. The first problem is defined in four zones defined by two straight lines that crosses perpendicularly. Here we consider two or four different linear systems. We prove that in a symmetric case (two systems) there exist systems with five limit cycles bifurcating far from the origin and in the n…
(Only some records are available in English at this moment)
Study of the Center-Focus Problem in Planar Analytic Differential Systems. Initially, to become familiar with the problem, we will study the case where the linear part is of the center type, which is due to Poincaré and Liapunov. Subsequently, the more challenging nilpotent case will be addressed. Additionally, an example of an orbitally symmetric nilpotent center will be sought, and a st…
The goal of the project is the study of planar vector fields with four invariant straight lines, two verticals and two horizontals, aiming its applications on game theory. The objective is to study the phase portraits, the bifurcation diagrans, the integrability of the system, the number of limit cycles, the algebricity and the hyperbolicity of the limit cycles and the annular periods of …
Introduce the student to the planar dynamic systems by studying the number of limit cycles that bifurcate from a linear center. In an initial phase, a study will be made on local aspects of the Qualitative Theory of Ordinary Differential Equations, with special emphasis on planar systems. In the sequence, a study of global aspects will be made, such as the notion of limit sets and attract…
The project aims to introduce the student to the Qualitative Theory of Ordinary Differential Equations. In a first phase, aspects of local theory will be addressed through the study of some classic results, such as: existence and uniqueness of solutions theorem, theorems of dependency in relation to initial conditions and parameters, flow defined by a differential equation, stable manifol…
In this postdoctoral project, we investigate the dynamics of global phenomena in systems governed by differential equations. More specifically, we study global connections in tridimensional Filippov systems and infinite dimensional Hamiltonian systems.
(Only some records are available in English at this moment)
Our main goal is to study the polycycles (also known as graphs) of vector fields with two vertical invariant straight lines and two horizontal invariant straight lines. Such family of vector fields is closely linked with Game Theory. More precisely, we aim to study the existence, genericity, stability, cyclicity and bifurcation diagrams of such polycycles. (AU)
Classification of global phase portraits of normal forms of reversible vector fields of type (2;1) of codimension zero and one. It is the exhibition of all possible global phase portraits of this class of vector fields on the Poincaré disk. The main tools are Hartman's Theorem, Center Manifold Theorem, Reversibility, Normal Forms, Blow up and Poincaré Compactification. (AU)
At first, this study aims to classify centers for a special class of piecewise smooth Ordinary Differential Equations defined in the unit sphere. In a second moment, we would like to obtain an upper bound for the number of limit cycles that bifurcate from the center. If this upper bound there exists, we will try to answer the question: how does it depend on the degree of the polynomial p…
(Only some records are available in English at this moment)
| 6 / 4 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 22 / 15 | Completed scholarships in Brazil |
| 7 / 6 | Completed scholarships abroad |
| 37 / 27 | All research grants and scholarships |
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