Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
We study the continuous and discontinuous planar piecewise differential systems formed by linear centres together with linear Hamiltonian saddles separated by one or two parallel straight lines. When these piecewise differential systems are either continuous or discontinuous separated by one straigh...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:267128 |
| Acceso en línea: | https://ddd.uab.cat/record/267128 https://dx.doi.org/urn:doi:10.1080/14689367.2022.2037519 |
| Access Level: | acceso abierto |
| Palabra clave: | Limit cycles Linear centers Linear Hamiltonian saddles Continuous piecewise linear differential systems Discontinuous piecewise differential systems First integrals |
| Sumario: | We study the continuous and discontinuous planar piecewise differential systems formed by linear centres together with linear Hamiltonian saddles separated by one or two parallel straight lines. When these piecewise differential systems are either continuous or discontinuous separated by one straight line, they have no limit cycles. When these piecewise differential systems are continuous and are separated by two parallel straight lines they do not have limit cycles. On the other hand, when these piecewise differential systems are discontinuous and separated by two parallel straight lines (either two centres and one saddle, or two saddles and one centre), we show that they can have at most one limit cycle, and that there exist such systems with one limit cycle. If the piecewise differential systems separated by two parallel straight lines have three linear centres or three linear Hamiltonian saddles it is known that they have at most one limit cycle. |
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