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arXiv · 1307.6825

On Poincar\'e-Bendixson Theorem and Non-Trivial Minimal Sets in Planar Nonsmooth Vector Fields

Tiago de Carvalho·Claudio A. Buzzi·Rodrigo D. Euzébio
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Abstract

In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. In the class of nonsmooth systems, that do not present sliding regions, a Poincar\'e-Bendixson Theorem is presented. A minimal set in planar Filippov systems not predicted in classical Poincar\'e-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.

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Tiago de Carvalho, Claudio A. Buzzi, Rodrigo D. Euzébio. 2013-07-25. On Poincar\'e-Bendixson Theorem and Non-Trivial Minimal Sets in Planar Nonsmooth Vector Fields. https://doi.org/10.5565/publmat6211806

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