New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2

Detalhes bibliográficos
Autor(a) principal: ITIKAWA,JACKSON
Data de Publicação: 2019
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=S0001-37652019000300202
Resumo: Abstract: We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. The first class is formed by the polynomials maps of the form (q(x)–p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f, g): R 2 ⟶ R 2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.
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spelling New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2 injective polynomial mapsglobal centerreal Jacobian conjectureplanar Hamiltonian systemsAbstract: We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. The first class is formed by the polynomials maps of the form (q(x)–p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f, g): R 2 ⟶ R 2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.Academia Brasileira de Ciências2019-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652019000300202Anais da Academia Brasileira de Ciências v.91 n.2 2019reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/0001-3765201920170627info:eu-repo/semantics/openAccessITIKAWA,JACKSONLLIBRE,JAUMEeng2019-06-27T00:00:00Zoai:scielo:S0001-37652019000300202Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2019-06-27T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
title New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
spellingShingle New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
ITIKAWA,JACKSON
injective polynomial maps
global center
real Jacobian conjecture
planar Hamiltonian systems
title_short New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
title_full New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
title_fullStr New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
title_full_unstemmed New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
title_sort New classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2
author ITIKAWA,JACKSON
author_facet ITIKAWA,JACKSON
LLIBRE,JAUME
author_role author
author2 LLIBRE,JAUME
author2_role author
dc.contributor.author.fl_str_mv ITIKAWA,JACKSON
LLIBRE,JAUME
dc.subject.por.fl_str_mv injective polynomial maps
global center
real Jacobian conjecture
planar Hamiltonian systems
topic injective polynomial maps
global center
real Jacobian conjecture
planar Hamiltonian systems
description Abstract: We present two new classes of polynomial maps satisfying the real Jacobian conjecture in ℝ 2. The first class is formed by the polynomials maps of the form (q(x)–p(y), q(y)+p(x)) : R 2 ⟶ R 2 such that p and q are real polynomials satisfying p'(x)q'(x) ≠ 0. The second class is formed by polynomials maps (f, g): R 2 ⟶ R 2 where f and g are real homogeneous polynomials of the same arbitrary degree satisfying some conditions.
publishDate 2019
dc.date.none.fl_str_mv 2019-01-01
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=S0001-37652019000300202
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652019000300202
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/0001-3765201920170627
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.91 n.2 2019
reponame:Anais da Academia Brasileira de Ciências (Online)
instname:Academia Brasileira de Ciências (ABC)
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instname_str Academia Brasileira de Ciências (ABC)
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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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