Limit cycles of discontinuous piecewise differential systems formed by two rigid systems separated by a straight line
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In this work we study the maximum number of limit cycles in some classes of discontinuous piecewise differential systems formed by two rigid systems separated by a straight line. These rigid systems are formed by a linear center plus a homogeneous polynomial of degree 2, 3, 4, 5, 6. For these classes of piecewise differential systems we solve the extended 16th Hilbert problem.
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LLIBRE, Jaume; SANCHEZ, Angela C. T.; TONON, Durval J. Limit cycles of discontinuous piecewise differential systems formed by two rigid systems separated by a straight line. Nonlinear Differential Equations and Applications, Berlin, v. 32, e48, 2025. DOI: 10.1007/s00030-025-01050-w. Disponível em: https://link.springer.com/article/10.1007/s00030-025-01050-w. Acesso em: 9 dez. 2025.