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On Poincaré–Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields

Buzzi, Claudio Aguinaldo ; de Carvalho, Tiago ; D. Euzébio, Rodrigo

Publicacions matemàtiques, 2018, Vol.62 (1), p.113-131 [Peer Reviewed Journal]

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Title:
On Poincaré–Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields
Author: Buzzi, Claudio Aguinaldo ; de Carvalho, Tiago ; D. Euzébio, Rodrigo
Is Part Of: Publicacions matemàtiques, 2018, Vol.62 (1), p.113-131
Description: 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.
Publisher: Universitat Autònoma de Barcelona
Language: Catalan;English

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