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| Home > Articles > Published articles > The extended 16th Hilbert problem for discontinuous piecewise linear centers separated by a nonregular line |
(Universidad de Sevilla. Departamento de Matemática Aplicada II) (Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)| Date: | 2021 |
| Abstract: | The study of the piecewise linear differential systems goes back to Andronov, Vitt and Khaikin in 1920's, and nowadays such systems still continue to receive the attention of many researchers mainly due to their applications. We study the discontinuous piecewise differential systems formed by two linear centers separated by a nonregular straight line. We provide upper bounds for the maximum number of limit cycles that these discontinuous piecewise differential systems can exhibit and we show that these upper bounds are reached. Hence, we solve the extended 16th Hilbert problem for this class of piecewise differential systems. |
| Grants: | Agencia Estatal de Investigación PGC2018-096265-B-I00 Agencia Estatal de Investigación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 |
| Note: | Altres ajuts: Consejería de Economía y Conocimiento de la Junta de Andalucía under grant P12-FQM-1658 |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | Discontinuous piecewise linear system ; Linear center ; Nonregular line |
| Published in: | International journal of bifurcation and chaos in applied sciences and engineering, Vol. 31, Issue 15 (December 2021) , art. 2150225, ISSN 1793-6551 |
9 p, 626.0 KB |
