The study of periodic orbits in piecewise continuous differential systems

• Grant number: 23/18276-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2024
• End date: February 28, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alex Carlucci Rezende
• Grantee: Gabriela Lye Watanabe
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 19/21181-0 - New frontiers in Singularity Theory, AP.TEM

Abstract

This project is proposed to a student entering the Master's course of the Graduate Program in Mathematics at UFSCar (PPGM-UFSCar). The candidate will graduate in Mathematics at UFSCar in February 2024 and was approved in the selection for the Master's course at PPGM-UFSCar. During her graduation, she studied several subjects of the Bachelor's degree in Mathematics and carried out three Scientific Initiation projects under the supervision of the same supervisor of this project. The themes of the SI projects were: 'Discrete Dynamic Systems', `'Metric Spaces and Introduction to Topology', and 'Introduction to Measure Theory and application in Ergodic Theory' (the latter with support from FAPESP) . This Master's project consists of initiating and deepening the candidate in the Qualitative Theory of Ordinary Differential Equations, providing the necessary support for the study of periodic orbits and limit cycles, both in continuous systems and, mainly, in piecewise continuous systems.