Invariant sets for piecewise smooth differential equations defined on two dimensional compact manifolds

• Grant number: 21/07017-2
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): September 01, 2021
• Effective date (End): August 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Beatriz Benatti da Rocha e Silva
• 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 will study families of piecewise smooth differential equations defined on compact two-dimensional manifolds $M$. Our main objective is to exhibit conditions for a piecewise polynomial system defined in $M$ to admit periodic orbits in cases where $M$ is the sphere or the torus. We will also study the structural stability in the case of piecewise smooth differential equations defined in a $M$ polyhedron, considering the possibilities for the sliding dynamics on the edges. (AU)