New lower bound for the Hilbert number in piecewise quadratic differential systems
We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by H (n) the extension of the...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:204398 |
| Acesso em linha: | https://ddd.uab.cat/record/204398 https://dx.doi.org/urn:doi:10.1016/j.jde.2018.09.032 |
| Access Level: | acceso abierto |
| Palavra-chave: | Non-smooth differential system Limit cycles in piecewise quadratic differential systems First and second order perturbations of isochronous quadratic systems Hilbert number for piecewise quadratic differential systems |
| Resumo: | We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by H (n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then H (2)≥16. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center. |
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