On Poincaré-Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields
Buzzi, Claudio (Universidade Estadual Paulista(Brazil). Departamento de Matemática)
de Carvalho, Tiago (Universidade Estadual Paulista(Brazil). Departamento de Matemática)
Euzébio, R (Universidade Estadual Paulista (Brasil). Departamento de Matemática)

Date:	2018
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Nonsmooth vector fields ; Poincaré-bendixson theory ; Minimal sets ; Limit sets
Published in:	Publicacions matemàtiques, Vol. 62 Núm. 1 (2018) , p. 113-131 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/329930
DOI: 10.5565/PUBLMAT6211806

19 p, 446.4 KB

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