The 16th Hilbert problem for discontinuous piecewise isochronous centers of degree one or two separated by a straight line

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(Universidad de Sevilla. Departamento de Matemática Aplicada II)
Llibre, Jaume

(Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973-

(Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))

Fecha:	2021
Resumen:	In this paper, we deal with discontinuous piecewise differential systems formed by two differential systems separated by a straight line when these two differential systems are linear centers (which always are isochronous) or quadratic isochronous centers. It is known that there is a unique family of linear isochronous centers and four families of quadratic isochronous centers. Combining these five types of isochronous centers, we obtain 15 classes of discontinuous piecewise differential systems. We provide upper bounds for the maximum number of limit cycles that these fifteen classes of discontinuous piecewise differential systems can exhibit, so we have solved the 16th Hilbert problem for such differential systems. Moreover, in seven of the classes of these discontinuous piecewise differential systems, the obtained upper bound on the maximum number of limit cycles is reached.
Ayudas:	Ministerio de Economía y Competitividad PGC2018-096265-B-I00 Ministerio de Ciencia e Innovación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Nota:	Altres ajuts: Consejería de Economía y Conocimiento de la Junta de Andalucía, under grant P12-FQM-1658
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió acceptada per publicar
Publicado en:	Chaos, Vol. 31, Issue 4 (April 2021) , art. 043112, ISSN 1089-7682

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