- Research Grants
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)
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...
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...
Dynamical systems are one of the best tools for understanding of the mathematical models of experimental sciences. The main goal of this project is to improve the knowledge of these systems obtaining new results with emphasis on the study of the following ten main topics: systems of differential equations piecewise smooth, discontinuous perturbations of centers, systems of quadratic pol...
The proposal is devoted to the study of piecewise smooth vector fields, in the case where the border of the smooth parts of the vector fields are not regular. In this context, it will be first made a study aimed at a classification of systems that are not structurally stable. Necessarily such a study requires an analysis of bifurcations of low codimension 1 and 2. Finally the project wi...
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.
Classification of the global phase portraits of the normal forms of the reversible vector fields of type (2; 0) of codimension zero and one. This is the exhibition of all possible global phase portraits of this class of vector fields on the Poincaré disk. We will use as tools: Hartman's Theorem, Center Manifold Theorem, Reversibility, Normal Forms, Blow up and Poincaré Compactification.
The project aims to introduce the student to the Qualitative Theory of Ordinary Differential Equations. In a first phase aspects of the local theory will be approached through the study of some classic results such as: existence and uniqueness theorem, theorems of dependence with respect to initial conditions and parameters, flow defined by a differential equation, the Grobman-Hartman ...
(Only some records are available in English at this moment)
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.
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...
Study aiming to obtain lower bound for the number of limit cycles for a special class of Ordinary Differential Equations piecewise smooth and defined in the cylinder. The main tool to be used is the Melnikov Theory. In a second moment, we analyze the regularization of such piecewise smooth systems by looking for smooth approximations that have the same amount of limiting cycles and whic...
Study of families of periodic orbits and their bifurcations in differential equations of finite dimension, with special attention to the following classes of systems of differential equations: (a) Polynomial differential systems in finite dimension and their limit cycles, and (b) piecewise linear differential systems (AU)
First part: study of the generic bifurcation of codimension one at the class reversible vector field of type (2n+1,n). More precisely, we intend to investigate the occurrence of families of periodic orbits and/or homo/heteroclinic orbits, by using the techniques of Normal Forms and Liapunov-Schmidt reduction. In sequence we will consider perturbation of such systems via KAM Theory and w...
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
|Data from Web of Science|
(References retrieved automatically from State of São Paulo Research Institutions)
EUZÉBIO, Rodrigo Donizete. Estudo de conjuntos minimais para sistemas descontínuos em dimensões 2 e 3. 134 f. Tese (Doutorado) - Universidade Estadual Paulista "Júlio de Mesquita Filho" Instituto de Biociencias, Letras e Ciencias Exatas. (10/18015-6)
TONON, Durval José. Um estudo global de campos de vetores planares. 167 f. Dissertação (Mestrado) - Instituto de Biociências, Letras e Ciências Exatas. Universidade Estadual Paulista. São José do Rio Preto. (04/11191-2)
ARAKAWA, Vinicius Augusto Takahashi. Um estudo de bifurcações de codimensão dois de campos de vetores. 104 f. Dissertação (Mestrado) - Instituto de Biociências, Letras e Ciências Exatas. Universidade Estadual Paulista. São José do Rio Preto. (05/57242-0)
CARVALHO, Tiago de. Conjuntos limite e bifurfações de campos de vetores suaves por partes no plano. 128 f. Tese (Doutorado) - Instituto de Biociências, Letras e Ciências Exatas. Universidade Estadual Paulista. São José do Rio Preto. (07/08707-5)
BUZZI, Claudio Aguinaldo. Formas normais de campos vetoriais reversiveis. Tese (Doutorado) - Instituto de Matemática, Estatística e Computação Científica. Universidade Estadual de Campinas (UNICAMP). (97/04728-4)
ALVES, Michele de Oliveira. Campos de vetores lineares reversíveis equivariantes. Dissertação (Mestrado) - Instituto de Biociências, Letras e Ciências Exatas. Universidade Estadual Paulista. São José do Rio Preto. (03/09874-1)