Limit cycles of discontinuous piecewise differential systems separated by a straight line and formed by cubic reversible isochronous centers having rational first integrals
Benabdallah, Imane (University Mohamed El Bachir. Department of Mathematics)
Benterki, Rebiha (University Mohamed El Bachir. Department of Mathematics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	A lot of attention has been paid in recent years to the study of piecewise differential systems, and more especially is studying the maximum number of limit cycles that these systems are able to exhibit. In this paper we consider all classes of discontinuous piecewise differential systems with cubic reversible isochronous centers having rational first integrals separated by the straight line x = 0. First, we solve the extension of the second part of the sixteenth Hilbert problem for each of the three classes of discontinuous piecewise differential systems formed by an arbitrary linear center and one of the three cubic reversible isochronous centers. We establish that, depending on the class presented, the maximum number of limit cycles of these classes varies between one and two. Second, by combining the three types of the cubic reversible isochronous centers, we obtain six classes of discontinuous piecewise differential systems formed by two cubic reversible isochronous centers. So we solve the extended sixteenth Hilbert problem for all these classes and we find the maximum number of limit cycles that such classes can exhibit. Moreover we have reinforced our results by giving examples for each class.
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Limit cycle ; Discontinuous piecewise differential systems ; Linear center ; Cubic reversible isochronous centers
Published in:	Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications and algorithms, Vol. 31, Num. 1b (2024) , p. 1-23, ISSN 1492-8760

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