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)
Data: |
2018 |
Resum: |
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. |
Drets: |
Tots els drets reservats. |
Llengua: |
Anglès |
Document: |
Article ; recerca ; Versió publicada |
Matèria: |
Nonsmooth vector fields ;
Poincaré-bendixson theory ;
Minimal sets ;
Limit sets |
Publicat a: |
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
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