CV Lattes
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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Bachelor's degree (2010), Master's degree (2012), and PhD (2015) in Mathematics from Universidade Estadual de Campinas, with a sandwich period at Universitat Autònoma de Barcelona (2014). Postdoctoral fellow at Universidade Estadual de Campinas and Universitat Autònoma de Barcelona (2015, 2016). Livre-Docência (habilitation) (2019) from Universidade Estadual de Campinas. Nowadays, Associate Professor (MS5.2) at Universidade Estadual de Campinas. Experience in Mathematics, focusing on Dynamic Systems, acting on the following subjects: bifurcation theory and discontinuous dynamical systems. (Source: Lattes Curriculum)
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In this research project, it will be addressed global aspects of differential equations and inclusions and it is divided into 2 main themes: 1. Bifurcation of Invariant Tori of Differential Equations and 2. Bifurcation of Periodic Solutions of Differential Systems with Low Regularity. In both themes, the main goal consists in developing methods for detecting periodic and quasi-periodic …
This project concerns on global aspects of nonsmooth differential equations, Lipschitz continuous and discontinuous. It is divided in 3 main subjects: Bifurcation of Limit Cycles, Bifurcation of Invariant Tori and Shilnikov Connections in Filippov Systems. Each subject presents several subprojects, which are concerned on distinct topics such as: averaging theory and Melnikov functions, ta…
This project aims to develop research in the field of nonsmooth differential equations. We are particularly interested in the sliding dynamics defined on the manifold of discontinuity. At a first moment, using the ideas from Melnikov, we study the bifurcation of a typical cycle of the Filippov systems. We also study the robustness of the chaotic behavior existing nearby a sliding Shilniko…
In this project, we tackle two problems concerning invariant tori for three-dimensional vector fields. The first one investigates the existence of invariant tori for vector fields having a 0-nilpotent singular point, i.e. vector fields whose linear term is yx. We propose the study of the invariant tori bifurcation for these vector fields using the Averaging theory to identify a Neimark-Sa…
Since the publication of Hilbert's list of problems, problem 16, concerning the maximum number H(n) (Hilbert number) of limit cycles of polynomial planar vector fields of degree n, has been one of the most important driving forces for new developments in the qualitative theory of vector fields. The finiteness of H(n), for n greater than or equal to 2, is still an open problem. The main ad…
Invariant manifolds are fundamental tools for understanding the qualitative behaviour of systems. Although the use of the averaging theory to find periodic orbits, a first example of non-trivial invariant sets, is well-established, there is still plenty to be done regarding the study of invariant sets of higher dimensions. In this area, Fenichel's Theory about the persistence of normally …
In this project, we aim to perform a qualitative study of some global aspects of Filippov systems. Using methods from the qualitative theory of dynamical systems, we shall address problems about the persistence of invariant sets (limit cycles, invariant tori, etc.) and the asymptotic behavior of solutions. More specifically, we shall consider a family F of non-smooth second order differen…
The main objective of this project consists in the study of limit cycles of continuous differential equations by means of topological tools such as the Brouwer degree and the coincidence degree. The theme of this project is strongly based on recent publications which generalize, for non-smooth differential equations, some classical techniques (Averaging Theory and Melnikov's Method) used …
It is intended in this project a qualitative study of the systems of differential equations. Problems will be addressed on the persistence of invariant and minimal sets (cycles, logs, cylinders, etc.) in perturbative differential systems. Such problems will enable the student to have contact with classical studies of the area, such as those dealing with persistence limit cycles and invari…
(Only some records are available in English at this moment)
In this project, we tackle two problems related to the cyclicity of limit periodic sets: The first one is concerns families of vector fields $X_\mu$ having a hyperbolic polycycle $\Gamma$ for $\mu_0$. When the return map is well defined in the region enclosed by $\Gamma$, there exists a monodromic singularity in this region. Our goal is to study the simultaneous cyclicity of both the poly…
The Averaging Theory provides tools for studying perturbative systems of differential equations. In particular, by studying the so-called averaged system, qualitative properties of the original perturbed system can be inferred. Most importantly, a number of results relate the existence of compact invariant manifolds of the averaged system with the existence of integral manifolds of the or…
Motivated by recent works generalizing the averaging theory for low regularity differential equations, this project proposes a higher order analysis for a family of perturbed Carathéodory differential equations aiming at finding sufficient conditions to guarantee the existence of periodic solutions of these equations that bifurcate from the non-perturbed system. It is also proposed to inv…
The second part of the Hilbert's sixteenth problem consists in determining the upper bound H(n) for the number of limit cycles that planar polynomial vector fields of degree n can have. For n greater than or equal 2, it is still unknown whether H(n) is finite or not. The main achievements obtained so far establish lower bounds for H(n). Regarding asymptotic behavior, the best result says…
(Only some records are available in English at this moment)
| 3 / 3 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 6 / 6 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 6 / 6 | Completed scholarships abroad |
| 19 / 19 | All research grants and scholarships |
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