On Poincaré-Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields
In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. A Poincaré-Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov systems not predicted in classical Poincaré-Bendixson theory and whose inter...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:182685 |
| Acceso en línea: | https://ddd.uab.cat/record/182685 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6211806 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonsmooth vector fields Poincaré-bendixson theory Minimal sets Limit sets |
| Sumario: | In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. A Poincaré-Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov systems not predicted in classical Poincaré-Bendixson theory and whose interior is non-empty is exhibited. The concepts of limit sets, recurrence, and minimal sets for nonsmoothsystems are defined and compared with the classical ones. Moreover some differences between them are pointed out. |
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