Periodic orbits in some piecewise differential systems

• Grant number: 23/09466-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: April 04, 2024
• End date: July 02, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Claudio Aguinaldo Buzzi
• Grantee: Claudio Aguinaldo Buzzi
• Visiting researcher: Joan Torregrosa I Arus
• Visiting researcher institution: Universitat Autònoma de Barcelona (UAB), Spain
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II, AP.TEM

Abstract

We will study problems related to the existence, nonexistence, and bifurcation of isolated periodic orbits (limit cycles) in planar piecewise polynomial systems. The first problem is the extension of Bendixson Dulac's theory in piecewise differential systems defined in two zones. The second is the simultaneous bifurcation of limit cycles near piecewise Hamiltonian centers with more than one period annulus. The third problem is related to the simultaneous invariant cones in 3D-piecewise differential systems. The last is related to the number of limit cycles in piecewise quadratic Kolmogorov planar systems. (AU)