On the Closing Lemma for planar piecewise smooth vector fields

Autor(es)

de Carvalho, Tiago

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 106, n. 6, p. 1174-1185, DEC 2016.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/02134-7 - Teoria qualitativa e bifurcações de campos de vetores suaves por partes
• Beneficiário: Tiago de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Regular