The solution of the second part of the 16th Hilbert problem for nine families of discontinuous piecewise differential systems

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(Université Mohamed El Bachir El Ibrahimi. Département de Mathématiques (Algeria))
Llibre, Jaume

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Fecha:	2020
Resumen:	We provide the maximum number of limit cycles of some classes of discontinuous piecewise differential systems formed by two differential systems separated by a straight line, when these differential systems are linear centers or three families of cubic isochronous centers, giving rise to ten different classes of discontinuous piecewise differential systems. These maximum number of limit cycles vary from 0, 1, 2, 3, 5, 7 and 12 depending on the chosen class. For nine of these classes, we prove that the corresponding maximum number of limit cycles are reached. In particular, we have solved the extension of the second part of the 16th Hilbert problem to these classes of discontinuous piecewise differential systems. The main tool used for proving these results is based on the first integrals of the systems which form the discontinuous piecewise differential systems.
Ayudas:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Materia:	Discontinuous piecewise differential systems ; Isochronous cubic systems ; Linear differential centers ; Limit cycle
Publicado en:	Nonlinear Dynamics, Vol. 102, Issue 4 (December 2020) , p. 2453-2466, ISSN 1573-269X

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