Scholarship 21/12630-5 - Sistemas dinâmicos, Variedades topológicas - BV FAPESP
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Cyclicity and local structural stability of piecewise vector fields

Grant number: 21/12630-5
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Start date: May 01, 2022
End date: April 30, 2026
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Regilene Delazari dos Santos Oliveira
Grantee:Ana Livia Rodero
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:19/21181-0 - New frontiers in Singularity Theory, AP.TEM
Associated scholarship(s):23/05686-0 - Integrability, center, and cyclicity problems for planar analytical vector fields, BE.EP.PD

Abstract

The main goal of this project is the study of piecewise smooth vector fields defined in 2, 3 and 4-dimensional manifolds, in two distinct lines which will be addressed simultaneously. The goal of the first line of this project is to study the cyclicity problem for a system having multiple period rings, searching for an upper bound for the number of limit cycles that can bifurcate, simultaneously, of these rings. For the second line, we consider a piecewise smooth vector field Y=(X^+, X^-) defined in a 3-dimensional manifold. We would like to characterize the local structurally stable singularities for the system Y when we suppose that both X^+ and X^- are completely integrable and that Y is refractive. In the same context, we consider a piecewise-smooth refractive system Y defined in R^4 (under the hypoteses that X^+ and X^- are completely integrable and Y is refractive) and we would like to give initial answers about local stability and local bifurcations of codimension 1. (AU)

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Scientific publications
(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)
BUZZI, CLAUDIO A.; RODERO, ANA LIVIA; TORREGROSA, JOAN. 3-dimensional piecewise linear and quadratic vector fields with invariant spheres. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 43, p. 27-pg., . (19/00440-7, 17/08779-8, 21/12630-5, 19/10269-3)
GARCIA, ISAAC A.; GINE, JAUME; RODERO, ANA LIVIA. Dulac functions and monodromic singularities. Journal of Mathematical Analysis and Applications, v. 547, n. 2, p. 14-pg., . (21/12630-5, 23/05686-0)
GARCIA, ISAAC A.; GINE, JAUME; RODERO, ANA LIVIA; YANG, XIAO. A NEW CHARACTERIZATION OF THE JACOBIAN CONJECTURE IN THE REAL PLANE AND SOME CONSEQUENCES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, v. N/A, p. 10-pg., . (21/12630-5, 23/05686-0)