The Extended 16th Hilbert Problem for Discontinuous Piecewise Systems Formed by Linear Centers and Linear Hamiltonian Saddles Separated by a Nonregular Line
We study discontinuous piecewise linear differential systems formed by linear centers and/or linear Hamiltonian saddles and separated by a nonregular straight line. There are two classes of limit cycles: the ones that intersect the separation line at two points and the ones that intersect the separa...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:299736 |
| Acesso em linha: | https://ddd.uab.cat/record/299736 https://dx.doi.org/urn:doi:10.1142/S0218127423501961 |
| Access Level: | acceso abierto |
| Palavra-chave: | Piecewise linear differential systems Discontinuity nonregular line Limit cycles |
| Resumo: | We study discontinuous piecewise linear differential systems formed by linear centers and/or linear Hamiltonian saddles and separated by a nonregular straight line. There are two classes of limit cycles: the ones that intersect the separation line at two points and the ones that intersect the separation line in four points, named limit cycles of type II2 and limit cycles of type II4, respectively. We prove that the maximum numbers of limit cycles of types II2 and II4 are two and one, respectively. We show that all these upper bounds are reached providing explicit examples. |
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