On the injectivity of C1 maps of the real plane

Detalhes bibliográficos
Autor(a) principal: Cobo, Milton [UNESP]
Data de Publicação: 2002
Outros Autores: Gutierrez, Carlos, Llibre, Jaume
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://cms.math.ca/10.4153/CJM-2002-045-0
http://hdl.handle.net/11449/67026
Resumo: Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.
id UNSP_aafe346927e1ed68af924ad52f548948
oai_identifier_str oai:repositorio.unesp.br:11449/67026
network_acronym_str UNSP
network_name_str Repositório Institucional da UNESP
repository_id_str 2946
spelling On the injectivity of C1 maps of the real planeLet X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.Departamento de Matemáticas IBILCE UNESP, Sao José do Rio Preto (SP)ICMC USP São Carlos IMPA, Rio de JaneiroDepartament de Matemàtiques Universitat Autonoma de Barcelona, 08193 Bellaterra, BarcelonaDepartamento de Matemáticas IBILCE UNESP, Sao José do Rio Preto (SP)Universidade Estadual Paulista (Unesp)Universidade de São Paulo (USP)Universitat Autonoma de BarcelonaCobo, Milton [UNESP]Gutierrez, CarlosLlibre, Jaume2014-05-27T11:20:32Z2014-05-27T11:20:32Z2002-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1187-1201http://cms.math.ca/10.4153/CJM-2002-045-0Canadian Journal of Mathematics, v. 54, n. 6, p. 1187-1201, 2002.0008-414Xhttp://hdl.handle.net/11449/67026WOS:0001797875000042-s2.0-0036972513Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCanadian Journal of Mathematics0.695info:eu-repo/semantics/openAccess2021-10-22T18:06:18Zoai:repositorio.unesp.br:11449/67026Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T14:01:25.212164Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On the injectivity of C1 maps of the real plane
title On the injectivity of C1 maps of the real plane
spellingShingle On the injectivity of C1 maps of the real plane
Cobo, Milton [UNESP]
title_short On the injectivity of C1 maps of the real plane
title_full On the injectivity of C1 maps of the real plane
title_fullStr On the injectivity of C1 maps of the real plane
title_full_unstemmed On the injectivity of C1 maps of the real plane
title_sort On the injectivity of C1 maps of the real plane
author Cobo, Milton [UNESP]
author_facet Cobo, Milton [UNESP]
Gutierrez, Carlos
Llibre, Jaume
author_role author
author2 Gutierrez, Carlos
Llibre, Jaume
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Universidade de São Paulo (USP)
Universitat Autonoma de Barcelona
dc.contributor.author.fl_str_mv Cobo, Milton [UNESP]
Gutierrez, Carlos
Llibre, Jaume
description Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.
publishDate 2002
dc.date.none.fl_str_mv 2002-12-01
2014-05-27T11:20:32Z
2014-05-27T11:20:32Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://cms.math.ca/10.4153/CJM-2002-045-0
Canadian Journal of Mathematics, v. 54, n. 6, p. 1187-1201, 2002.
0008-414X
http://hdl.handle.net/11449/67026
WOS:000179787500004
2-s2.0-0036972513
url http://cms.math.ca/10.4153/CJM-2002-045-0
http://hdl.handle.net/11449/67026
identifier_str_mv Canadian Journal of Mathematics, v. 54, n. 6, p. 1187-1201, 2002.
0008-414X
WOS:000179787500004
2-s2.0-0036972513
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Canadian Journal of Mathematics
0.695
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 1187-1201
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128305051729920

Registros relacionados