| Grant number: | 21/14695-7 |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| Effective date (Start): | February 01, 2022 |
| Effective date (End): | January 31, 2026 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Principal Investigator: | Regilene Delazari dos Santos Oliveira |
| Grantee: | Yagor Romano Carvalho |
| Host Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
| Associated research grant: | 19/21181-0 - New frontiers in Singularity Theory, AP.TEM |
| Associated scholarship(s): | 22/03800-7 - Study of math epidemiological models in piecewise smooth systems and regularization, BE.EP.PD |
Abstract The present project has four main lines of research for planar differential systems. First, in a generic situation, we intend to understand the behavior of the regularization of orbits of a piecewise smooth system with four zones, near of a singular point in the discontinuity manifold having an orbit of the "homoclinic type". In a second moment, assuming conditions for the existence of this "homoclinic type" orbit, seek conditions for the existence of limit cycles of the regularized field. Piecewise smooth Hamiltonian systems allow more configurations of centers, so in a third front, we dedicate to the study of aspects and calculation of the period function for this type of systems. Finally, in a fourth approach we will study new versions of Hilbert's sixteenth problem, i.e. to find a lower bound to the number of limit cycles in terms of the number of homogeneous vector fields formed by single monomials involved in polynomial differential systems. | |
| News published in Agência FAPESP Newsletter about the scholarship: | |
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