On Poincaré–Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields
- Autores: Claudio A. Buzzi, Tiago de Carvalho, Rodrigo D. Euzébio
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 62, Nº 1, 2018, págs. 113-131
- Idioma: inglés
- DOI: 10.5565/329930
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Resumen
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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