3-dimensional piecewise linear and quadratic vector fields with invariant spheres
We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:303170 |
| Acceso en línea: | https://ddd.uab.cat/record/303170 https://dx.doi.org/urn:doi:10.14232/ejqtde.2024.1.43 |
| Access Level: | acceso abierto |
| Palabra clave: | Piecewise smooth vector fields with invariant spheres Invariant cones 1-parameter families of closed trajectories |
| Sumario: | We consider the class X of 3-dimensional piecewise smooth vector fields that admit a first integral which leaves invariant any sphere centered at the origin. In this class, we prove that a linear vector field does not admit isolated invariant cones. Moreover, we provide the existence of at least ten 1-parameter families of crossing closed trajectories for quadratic vector fields in X. |
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