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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON POINCARE BENDIXSON THEOREM AND NON-TRIVIAL MINIMAL SETS IN PLANAR NONSMOOTH VECTOR FIELDS

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Author(s):
Buzzi, Claudio A. [1] ; Carvalho, Tiago [2] ; Euzebio, Rodrigo D. [1]
Total Authors: 3
Affiliation:
[1] Univ Estadual Paulista, IBILCE, BR-15054000 Sao Paulo - Brazil
[2] Univ Estadual Paulista, FC, BR-17033360 Sao Paulo - Brazil
Total Affiliations: 2
Document type: Journal article
Source: PUBLICACIONS MATEMATIQUES; v. 62, n. 1, p. 113-131, 2018.
Web of Science Citations: 3
Abstract

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. (AU)

FAPESP's process: 13/24541-0 - Ergodic and qualitative theory of dynamical systems
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 14/18508-3 - Minimal sets of piecewise differential systems in dimension 3
Grantee:Rodrigo Donizete Euzébio
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 13/25828-1 - Minimal sets and invariant manifolds in piecewise smooth systems
Grantee:Rodrigo Donizete Euzébio
Support Opportunities: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 14/02134-7 - Qualitative theory and bifurcations of piecewise smooth vector fields
Grantee:Tiago de Carvalho
Support Opportunities: Regular Research Grants