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...

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Bibliographic Details
Published in:Publicacions matemàtiques 2018-01, Vol.62 (2), p.113-131
Main Authors: Buzzi, Claudio A., Carvalho, Tiago, Euzébio, Rodrigo D.
Format: Article
Language:English
Online Access:Get full text
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Summary: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 nonsmooth systems are defined and compared with the classical ones. Moreover some differences between them are pointed out.
ISSN:0214-1493
2014-4350