Invariant sets and chaotic behavior in piecewise smooth dynamical systems on compact manifolds of low dimension

• Grant number: 22/07654-5
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: December 01, 2022
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Tiago Miguel Pires de Abreu
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/13481-0 - Geometry of control, dynamical and stochastic systems, AP.TEM
• Associated scholarship(s): 24/21067-0 - Bifurcation of Limit Cycles from Polycycles in Dynamical Systems, BE.EP.DR

Abstract

In this project, we study piecewise smooth dynamical systems using the Filippov convention. Our focus will be on dynamical systems defined in low dimensional compact manifolds. We are interested in the existence of minimal sets for these systems. Moreover, we want to classify such systems in termos of the chaotic behavior. In particular, we will study the global dynamics of piecewise smooth dynamical systems in bidimensional torus.

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)

DE ABREU, TIAGO M. P.; MARTINS, RICARDO M.. Estimates for the Number of Limit Cycles in Discontinuous Generalized Liénard Equations. Qualitative Theory of Dynamical Systems, v. 23, n. 4, p. 14-pg., 2024-09-01. (18/03338-6, 21/08031-9, 22/07654-5)