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

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

ISSN: 0214-1493 ;EISSN: 2014-4350 ;DOI: 10.5565/PUBLMAT6211806

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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
  • Identifier: ISSN: 0214-1493
    EISSN: 2014-4350
    DOI: 10.5565/PUBLMAT6211806
  • Source: Alma/SFX Local Collection
    Revistes Catalanes amb Accés Obert (RACO)
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