The extended 16th Hilbert problem for a class of discontinuous piecewise differential systems
In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applic...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:274779 |
| Acceso en línea: | https://ddd.uab.cat/record/274779 https://dx.doi.org/urn:doi:10.1007/s11071-022-07891-9 |
| Access Level: | acceso abierto |
| Palabra clave: | Limit cycle Discontinuous piecewise linear differential systems Linear differential center Hamiltonian isochronous global center |
| Sumario: | In order to understand the dynamics of the planar differential systems, the limit cycles play a main role, but in general their study is not easy. These last years, an increasing interest appeared for studying the limit cycles of some classes of piecewise differential systems, due to the rich applications of this kind of differential systems. This paper solves the extended 16th Hilbert problem for a family of discontinuous planar differential systems with two regions separated by the straight line x= 0. By using the first integrals, we prove that the maximum number of crossing limit cycles in the family of systems formed by a linear center and a class of Hamiltonian isochronous global center with a polynomial first integral of degree 2n is 5. |
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