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
• Effective date (Start): December 01, 2022
• Effective date (End): February 28, 2026
• 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

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.