A new qualitative proof of a result on the real jacobian conjecture

Detalhes bibliográficos
Autor(a) principal: BRAUN,FRANCISCO
Data de Publicação: 2015
Outros Autores: LLIBRE,JAUME
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Anais da Academia Brasileira de Ciências (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000401519
Resumo: Let F= (f, g) : R2 → R2be a polynomial map such that det DF(x) is different from zero for all x∈ R2. We assume that the degrees of fand gare equal. We denote by the homogeneous part of higher degree of f and g, respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If do not have real linear factors in common, then F is injective.
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spelling A new qualitative proof of a result on the real jacobian conjectureReal Jacobian conjectureglobal injectivitycenterPoincaré compactificationLet F= (f, g) : R2 → R2be a polynomial map such that det DF(x) is different from zero for all x∈ R2. We assume that the degrees of fand gare equal. We denote by the homogeneous part of higher degree of f and g, respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If do not have real linear factors in common, then F is injective.Academia Brasileira de Ciências2015-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000401519Anais da Academia Brasileira de Ciências v.87 n.3 2015reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/0001-3765201520130408info:eu-repo/semantics/openAccessBRAUN,FRANCISCOLLIBRE,JAUMEeng2015-09-22T00:00:00Zoai:scielo:S0001-37652015000401519Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2015-09-22T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv A new qualitative proof of a result on the real jacobian conjecture
title A new qualitative proof of a result on the real jacobian conjecture
spellingShingle A new qualitative proof of a result on the real jacobian conjecture
BRAUN,FRANCISCO
Real Jacobian conjecture
global injectivity
center
Poincaré compactification
title_short A new qualitative proof of a result on the real jacobian conjecture
title_full A new qualitative proof of a result on the real jacobian conjecture
title_fullStr A new qualitative proof of a result on the real jacobian conjecture
title_full_unstemmed A new qualitative proof of a result on the real jacobian conjecture
title_sort A new qualitative proof of a result on the real jacobian conjecture
author BRAUN,FRANCISCO
author_facet BRAUN,FRANCISCO
LLIBRE,JAUME
author_role author
author2 LLIBRE,JAUME
author2_role author
dc.contributor.author.fl_str_mv BRAUN,FRANCISCO
LLIBRE,JAUME
dc.subject.por.fl_str_mv Real Jacobian conjecture
global injectivity
center
Poincaré compactification
topic Real Jacobian conjecture
global injectivity
center
Poincaré compactification
description Let F= (f, g) : R2 → R2be a polynomial map such that det DF(x) is different from zero for all x∈ R2. We assume that the degrees of fand gare equal. We denote by the homogeneous part of higher degree of f and g, respectively. In this note we provide a proof relied on qualitative theory of differential equations of the following result: If do not have real linear factors in common, then F is injective.
publishDate 2015
dc.date.none.fl_str_mv 2015-09-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000401519
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000401519
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0001-3765201520130408
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Academia Brasileira de Ciências
publisher.none.fl_str_mv Academia Brasileira de Ciências
dc.source.none.fl_str_mv Anais da Academia Brasileira de Ciências v.87 n.3 2015
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
instacron:ABC
instname_str Academia Brasileira de Ciências (ABC)
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institution ABC
reponame_str Anais da Academia Brasileira de Ciências (Online)
collection Anais da Academia Brasileira de Ciências (Online)
repository.name.fl_str_mv Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)
repository.mail.fl_str_mv ||aabc@abc.org.br
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