Piecewise smooth differential equations in dimension 3

• Grant number: 18/25575-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2019
• End date: January 14, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Joyce Aparecida Casimiro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 22/01375-7 - Limit cycles of discontinuous piecewise smooth differential systems in the plane R2 and in the space R3, BE.EP.DR

Abstract

The aim of this project is to study systems of piecewise smooth differential equations in dimension 3, locally and globally (in $\mathbb R^3$ and also in compact manifolds). The expected results are about structural stability and chaotic behavior of these systems. Moreover, we want to study the relations between Sotomayor-Teixeira Regularization and Singular Perturbation Theory problems associated to these systems. (AU)

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)

CASIMIRO, JOYCE A.; LLIBRE, JAUME. Limit Cycles of Continuous Piecewise Smooth Differential Systems. Results in Mathematics, v. 78, n. 5, p. 14-pg., 2023-10-01. (22/01375-7, 18/25575-0)

CASIMIRO, JOYCE A.; LLIBRE, JAUME. Limit cycles of discontinuous piecewise differential Hamiltonian systems separated by a circle, or a parabola, or a hyperbola. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 225, p. 10-pg., 2024-05-31. (22/01375-7, 18/25575-0)

CASIMIRO, JOYCE A.; MARTINS, RICARDO M.; NOVAES, DOUGLAS D.. POINCARE-HOPF THEOREM FOR FILIPPOV VECTOR FIELDS ON 2-DIMENSIONAL COMPACT MANIFOLDS. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v. 23, n. 11, p. 27-pg., 2024-08-24. (18/03338-6, 19/10269-3, 22/09633-5, 21/08031-9, 18/13481-0, 18/25575-0, 22/01375-7)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CASIMIRO, Joyce Aparecida. Campos vetoriais suaves por partes: índice de singularidades e alguns resultados sobre a existência de ciclos limites. 2024. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.