CV Lattes
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Universidade de São Paulo (USP). Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP) (Institutional affiliation from the last research proposal) Birthplace: Brazil
bachelor's at Bacharelado Em Matemática from Universidade Estadual Paulista Júlio de Mesquita Filho (2004), master's at Mathematics from Universidade de São Paulo (2007) and doctorate at Applied Mathematics from Universidade Estadual Paulista Júlio de Mesquita Filho (2011). He is currently full professor at Universidade Estadual Paulista. He was associated professor at Universidade de São Paulo andat Estadual Paulista Júlio de Mesquita Filho. Has experience in Mathematics, focusing on Dynamic Systems, acting on the following subjects: piecewise smooth vector fields, bifurcations, structural stability. (Source: Lattes Curriculum)
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In this research project we will be interested in studying new topics related to continuous-time dynamical systems. We will seek both theoretical results and applications in areas such as: Biology, Engineering and Economics. Among the main results to be studied we quote: dynamics of evolution models of diseases such as cancer, HIV-AIDS and COVID-19; obtaining minimal sets for piecewise sm…
In this research project we will beinterested in studying new topics related to continuous time Dynamical Systems. We will seek both theoretical results and applications in areas such as: Biology, Engineering and Economics. Among the main results to be studied are: dynamics of evolution models of diseases such as cancer, HIV-AIDS and COVID-19; obtaining minimal sets for piecewise smooth v…
In this research project we will beinterested in studying unpublished topics related to the Qualitative Theory of Ordinary Differential Equations. When we consider smooth vector fields, it is a classic and very relevant research topic, to determine the possible existence of points to which the orbit returns infinite many times in its neighborhood. The Closing Lemma seeks to establish when…
(Only some records are available in English at this moment)
In this project we will have the scientific initiation article [CarLei] as the base text. In the theoretical part, we will study the Grobman-Hartmann Theorem, how to obtain phase portraitsof smooth vector fields (based on eigenvalues or eigenvectors), among others.In terms of applications in Economics, we will study the models: Palomba, ContinuousOligopoly, Continuous IS-LM, Tobin-Blancha…
We will study the classical work of Filippov, and other recent papers, concerning differential inclusions. Such theory is known as Filippov's convention.
We will address one of the most challenging problems in the dynamical systems theory which is called "Closing Lemma". The problem statement is as follows:Consider a non-periodic point x0 such that the trajectory through x0 returns to a neighborhood ofx0 infinite times. There is a small disturbation of the original system so that the newsystem has a closed orbit passing through x0 ?This pr…
(Only some records are available in English at this moment)
In this project we will study an introduction concerning piecewise smooth vector fields. These dynamical systems are very used to model realistic problems where a kind of "on-off" process is considered.
We will study the qualitative theory of ordinary differential equations (ODEs) addressing a series of classical theorems that will alert the candidate to which propertiesare desirable (stability, convergence, hyperbolicity, etc) in ODE systems.We will approach the qualitative/geometric theory introduced in the 19th century by Henri Poincaré. To get to thatobjective, it will be necessary t…
In this project we will study properties of discrete dynamical systems using the 10 first sections of the book A first course in chaotic dynamical systems, Series: Addison-Wesley studies in nonlinearity, Robert L. Devaney.
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing grants |
| 6 / 6 | Completed research grants |
| 4 / 4 | Ongoing scholarships in Brazil |
| 20 / 18 | Completed scholarships in Brazil |
| 31 / 29 | All research grants and scholarships |
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