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
bachelor's at Bacharelado em Matemática from Universidade Federal do Rio Grande do Sul (1988), master's at Mathematics from Universidade Federal do Rio Grande do Sul (1989) and doctorate at Mathematics from Universidade de São Paulo (1997). Has experience in Mathematics, focusing on Dynamic Systems, acting on the following subjects: campos de vetores, sistemas dinâmicos, campos de vetores descontínuos, ciclos limites and perturbações singulares. (Source: Lattes Curriculum)
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In recent years, there has been intense scientific activity in the development of a qualitative theory for piecewise smooth dynamical systems, in the spirit of Poincaré's work. We will apply the geometric singular perturbation theory and slow-fast systems for the development of this study. (AU)
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…
A finite set of vector fields, defines a piecewise-smooth vector field X on a manifold M and switching set E. A regularization is a 1-parameter family of smooth vector fields, converging to X, when the parameter goes to zero.We study regularization processes when the switching set is a regular surface and when its singular set is not empty. We introduce the concept of discontinuously fo…
(Only some records are available in English at this moment)
First, we will discuss properties of Shilnikov sliding connections in Filippov fields. We will analyze behavior in high dimensions, complexity (dimensionality) in variations of a parameter, and homotopic types of closed orbits.Second, we will discuss the relationship between hyperbolic cocycles and difference/differential equations with exponential dichotomy, as well as properties arising…
Nonlinear dynamics is an essential tool for studying biological systems, as many biological processes exhibit nonlinear behavior due to interactions between variables. Ordinary Differential Equations are used in several models. In particular in population growth models (Malthusian, logistic) and epidemiological models (SIR). In this project we will study the main results of the Qualitativ…
We will study the behavior of the orbits of the regularized systems around tangential degenerate singularities using the techniques of geometric theory of singular perturbations.We will investigate the regularization of tangential polycycles for Filippov systems.We will also study piecewise Holomorphic systems.
We will study flows on invariant algebraic surfaces via analysis of systems with impasses. We will investigate the connexion of such problems with the Geometric Theory of Singular Perturbation. We will look for conditions that guarantee the existence of minimal sets and invariant manifolds of systems with symmetries. (AU)
We will study Ordinary Differential Equations (EDOS's) and their applications in models derived from biology. The modeling allows to describe the behavior of the systems. We will mainly analyze the dynamic aspects. We will start with a complete study of linear equations and then we will study the non-linear equations using the phase plane. We will see how to deduce the characteristics of …
(Only some records are available in English at this moment)
We will study the number of limit cycles of piecewise holomorphic systems, which is related to the famous Hilbert Problem 16 for piecewise vector fields. Also, we will investigate slow-fast systems in C^2, which can be used in the regularization process of discontinuous fields in R^4 with discontinuity surface with codimension 2. Also, we are interested in investigating the typical singul…
Our main goal in this project is to perturbation Kolmogorov Systems on planar piecewise vector fields defined in two zones separated by a straight line and study how many limit cycles can be obtained.In addition, we intend to approach the Kolmogorov Systems through Sotomayor-Teixeira regularization. It is well known that different regularizations can lead to different ways of defining sli…
Our main goal is to study constrained systems. Applications for this class of systems can be found in physical models, such as electrical circuits. It is also possible to find constrained systems in another mathematical contexts, for example, in the study of the flows of smooth vector fields on invariant manifolds. We intend to investigate how we can describe these flows by using such sys…
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing grants |
| 6 / 5 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 12 / 7 | Completed scholarships in Brazil |
| 4 / 4 | Completed scholarships abroad |
| 25 / 19 | All research grants and scholarships |
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