Johana Jimenez, Jaume Llibre, Joao C. Medrado
In previous years the study of the version of Hilbert's 16th problem for piecewise linear differential systems in the plane has increased. There are many papers studying the maximum number of crossing limit cycles when the differential system is defined in two zones separated by a straight line. In particular in [11,13] it was proved that piecewise linear differential centers separated by a straight line have no crossing limit cycles. However in [14,15] it was shown that the maximum number of crossing limit cycles of piecewise linear differential centers can change depending of the shape of the discontinuity curve. In this work we study the maximum number of crossing limit cycles of piecewise linear differential centers separated by a conic.differential centers separated by a conic
Submitted March 20, 2019. Published May 7, 2020.
Math Subject Classifications: 34C05, 34C07, 37G15.
Key Words: Discontinuous piecewise linear differential centers; limit cycles; conics.
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| Johana Jimenez |
Universidade Federal do Oeste da Bahia
46470000 Bom Jesus da Lapa, Bahia, Brazil
| Jaume Llibre |
Departament de Matemàtiques
Universitat Autónoma de Barcelona
08193 Bellaterra, Barcelona, Catalonia, Spain
João C. Medrado |
Instituto de Matemática e Estatística
Universidade Federal de Goiás
74001-970 Goiânia, Goiás, Brazil
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