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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Jackson is a professor and researcher at the Department of Statistics, Physcis and Mathematics of the Universidade Federal de São João del-Rey, campus Alto Paraopeba. His research is in the field of dynamical systems, working mainly on qualitative theory of ordinary differential equations. Jackson was a postdoctoral fellow at the Institute of Mathematics and Computer Science (ICMC) of the University of São Paulo (USP), São Carlos (2016), with a research internship at the Universitat Autònoma de Barcelona, #8203;#8203;Spain (2017). He holds a bachelor's degree (2009) and a master's (2012) in Mathematics from ICMC/USP - São Carlos, with a PhD in Mathematics from the Universitat Autònoma de Barcelona, #8203;#8203;Spain (2015). He is a member of the Brazilian Mathematical Society. (Source: Lattes Curriculum)
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In this project we aim to investigate the uniform isochronous centers in planar differential systems of degree 5. In particular, we want to study necessary and sufficient conditions to characterize such systems, to provide a classification of their global phase portraits in the Poincaré disc, and also to analyze the bifurcation of limit cycles when the uniform isochronous center is pertur…
One classic problem in the qualitative theory of ordinary differential equations (ODE's) is the local planar singular point caracterization of vector systems. This problem is completely solved, except to the monodromic case, where the orbits turn around the singular point.In analytic differential systems, a monodromic singular point is either a center or a focus. The investigation that de…
Main objective of this project is to introduce the student to two known problems of the qualitative theory of ordinary differential equations, the center-focus problem and the XVI Hilbert Problem, weak version.
Let F=(f,g) be a polynomial map with nonvanishing Jacobian determinant, such that F(0,0)=(0,0). This project aims to apply results from the dynamical systems theory in order to determine if there exists a counterexample to the real Jacobian conjecture with f and g of degree 5, which is so far the lower degree of a such counterexample could exist.
| 4 / 3 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 5 / 4 | All Scholarships |
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