On the Closing Lemma for planar piecewise smooth vector fields

de Carvalho, Tiago

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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 the Closing Lemma for planar piecewise smooth vector fields

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Author(s):	de Carvalho, Tiago Total Authors: 1
Document type:	Journal article
Source:	JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 106, n. 6, p. 1174-1185, DEC 2016.
Web of Science Citations:	0
Abstract
A large number of papers deal with ``Closing Lemmas{''} for C-r-vector fields (and C-r-diffeomorphisms). Here, we introduce this subject and formalize the terminology about nontrivially recurrent points and nonwandering points for the context of planar piecewise smooth vector fields. A global bifurcation analysis of a special family of piecewise smooth vector fields presenting a nonwandering set with nontrivial recurrence is performed. As a consequence, we are able to say that the Classical and the Improved Closing Lemmas are false for this scenario. (C) 2016 Elsevier Masson SAS. All rights reserved. (AU)

FAPESP's process:	14/02134-7 - Qualitative theory and bifurcations of piecewise smooth vector fields
Grantee:	Tiago de Carvalho
Support Opportunities:	Regular Research Grants

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