Journal
PUBLICACIONS MATEMATIQUES
Volume 62, Issue 1, Pages 113-131Publisher
UNIV AUTONOMA BARCELONA
DOI: 10.5565/PUBLMAT6211806
Keywords
Nonsmooth vector fields; Poincare Bendixson theory; minimal sets; limit sets
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Funding
- FAPESP-BRAZIL [2013/24541-0]
- CAPES/Brazil (program PROCAD) [88881.068462/2014-01]
- Sao Paulo Research Foundation (FAPESP) [2014/02134-7, 2013/25828-1, 2014/18508-3]
- CAPES/Brazil [88881.030454/2013-01, 1576689, 478230/2013-3, 443302/2014-6]
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In this paper some qualitative and geometric aspects of nonsmooth vector fields theory are discussed. A Poincare-Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov systems not predicted in classical Poincare-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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