Johana Jimenez, Jaume Llibre, Joao C. Medrado
Abstract:
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.
DOI: 10.58997/ejde.2020.41
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Johana Jimenez Universidade Federal do Oeste da Bahia 46470000 Bom Jesus da Lapa, Bahia, Brazil email: jjohanajimenez@gmail.com |
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Jaume Llibre Departament de Matemàtiques Universitat Autónoma de Barcelona 08193 Bellaterra, Barcelona, Catalonia, Spain email: jllibre@mat.uab.cat |
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João C. Medrado Instituto de Matemática e Estatística Universidade Federal de Goiás 74001-970 Goiânia, Goiás, Brazil email: medrado@ufg.br, joaocarlosmedrado@gmail.com |
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