Bifurcation of invariant manifolds in smooth and non-smooth differential systems

• Grant number: 23/04851-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2023
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marco Antônio Teixeira
• Grantee: Nasrin Sadri
• 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

This research project is divided into two parts. The first part is related to the detection of periodic orbits and torus bifurcation by using averaging theory as systematic. Further, we investigate the interaction between normal form theory and averaging theory. The second part is about the calculation of orbital normal form for differential systems with Bogdanov-Takens and Hopf singulariies and, also, studying possible bifurcations, especially the detection of periodic solutions and torus bifurcation. Bifurcations in non-smooth differential system, such as polycycles, Shilnikov connections, and Bykov connections, as well as their regularizations, will also be object of investigation.