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Limit cycles, regularization and period function of piecewise smooth planar systems.

Grant number: 21/14695-7
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): February 01, 2022
Effective date (End): January 31, 2025
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


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.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BUZZI, CLAUDIO A.; CARVALHO, YAGOR ROMANO; LLIBRE, JAUME. Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centres. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 37, n. 4, p. 19-pg., . (21/14695-7, 16/00242-2, 19/10269-3, 18/05098-2)

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