Dynamical systems with symmetries and implicit differential equations

• Grant number: 20/04717-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: June 01, 2020
• End date: January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Paulo Ricardo da Silva
• Grantee: Luiz Fernando da Silva Gouveia
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM
• Associated scholarship(s): 22/03801-3 - Lower bounds for local cyclicity for Kolmogorov systems on planar piecewise vector fields, BE.EP.PD

Abstract

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)

Scientific publications

(7)

(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)

GOUVEIA, LUIZ F. S.; TORREGROSA, JOAN. Local cyclicity in low degree planar piecewise polynomial vector fields. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 60, AUG 2021. (20/04717-0)

GOUVEIA, LUIZ F. S.; RONDON, GABRIEL; SILVA, PAULO R. DA. Piecewise holomorphic systems. Journal of Differential Equations, v. 332, p. 33-pg., 2022-09-25. (20/04717-0, 20/06708-9, 19/10269-3)

GOUVEIA, LUIZ F. S.; TORREGROSA, JOAN. THE LOCAL CYCLICITY PROBLEM: MELNIKOV METHOD USING LYAPUNOV CONSTANTS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. N/A, p. 20-pg., 2022-04-19. (20/04717-0)

GOUVEIA, LUIZ F. S.; DA SILVA, PAULO R. R.; RONDON, GABRIEL. Global Phase Portrait and Local Integrability of Holomorphic Systems. Qualitative Theory of Dynamical Systems, v. 22, n. 1, p. 26-pg., 2023-03-01. (20/06708-9, 19/10269-3, 20/04717-0)

GOUVEIA, LUIZ F. S.; TORREGROSA, JOAN. Lower bounds for the local cyclicity of centers using high order developments and parallelization. Journal of Differential Equations, v. 271, p. 447-479, JAN 15 2021. (20/04717-0)

GINE, JAUME; GOUVEIA, LUIZ F. S.; TORREGROSA, JOAN. Lower bounds for the local cyclicity for families of centers. Journal of Differential Equations, v. 275, p. 309-331, FEB 25 2021. (20/04717-0)

GOUVEIA, LUIZ F. S.; QUEIROZ, LUCAS. Lower bounds for the cyclicity of centers of quadratic three-dimensional systems. Journal of Mathematical Analysis and Applications, v. 530, n. 1, p. 16-pg., 2024-02-01. (22/03801-3, 20/04717-0, 19/13040-7, 21/14450-4)