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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


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)

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