Topological equivalence for multiple saddle connections

Detalhes bibliográficos
Autor(a) principal: ALONSO,CLEMENTA
Data de Publicação: 2002
Outros Autores: CAMACHO,MARIA IZABEL, CANO,FELIPE
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=S0001-37652002000400002
Resumo: We study the topological equivalence between two vector fields defined in the neighborhood of the skeleton of a normal crossings divisor in an ambient space of dimension three. We deal with singularities obtained from local ones by ambient blowing-ups: we impose thus the non-degeneracy condition that they are all hyperbolic without certain algebraic resonances in the set of eigenvalues. Once we cut-out the attractors, we get the result if the corresponding graph has no cycles. The case of cycles is of another nature, as the Dulac Problem in dimension three.
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spelling Topological equivalence for multiple saddle connectionssaddle connectionssingular vector fieldstopological equivalenceblowing upsWe study the topological equivalence between two vector fields defined in the neighborhood of the skeleton of a normal crossings divisor in an ambient space of dimension three. We deal with singularities obtained from local ones by ambient blowing-ups: we impose thus the non-degeneracy condition that they are all hyperbolic without certain algebraic resonances in the set of eigenvalues. Once we cut-out the attractors, we get the result if the corresponding graph has no cycles. The case of cycles is of another nature, as the Dulac Problem in dimension three.Academia Brasileira de Ciências2002-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000400002Anais da Academia Brasileira de Ciências v.74 n.4 2002reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652002000400002info:eu-repo/semantics/openAccessALONSO,CLEMENTACAMACHO,MARIA IZABELCANO,FELIPEeng2003-01-24T00:00:00Zoai:scielo:S0001-37652002000400002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2003-01-24T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false
dc.title.none.fl_str_mv Topological equivalence for multiple saddle connections
title Topological equivalence for multiple saddle connections
spellingShingle Topological equivalence for multiple saddle connections
ALONSO,CLEMENTA
saddle connections
singular vector fields
topological equivalence
blowing ups
title_short Topological equivalence for multiple saddle connections
title_full Topological equivalence for multiple saddle connections
title_fullStr Topological equivalence for multiple saddle connections
title_full_unstemmed Topological equivalence for multiple saddle connections
title_sort Topological equivalence for multiple saddle connections
author ALONSO,CLEMENTA
author_facet ALONSO,CLEMENTA
CAMACHO,MARIA IZABEL
CANO,FELIPE
author_role author
author2 CAMACHO,MARIA IZABEL
CANO,FELIPE
author2_role author
author
dc.contributor.author.fl_str_mv ALONSO,CLEMENTA
CAMACHO,MARIA IZABEL
CANO,FELIPE
dc.subject.por.fl_str_mv saddle connections
singular vector fields
topological equivalence
blowing ups
topic saddle connections
singular vector fields
topological equivalence
blowing ups
description We study the topological equivalence between two vector fields defined in the neighborhood of the skeleton of a normal crossings divisor in an ambient space of dimension three. We deal with singularities obtained from local ones by ambient blowing-ups: we impose thus the non-degeneracy condition that they are all hyperbolic without certain algebraic resonances in the set of eigenvalues. Once we cut-out the attractors, we get the result if the corresponding graph has no cycles. The case of cycles is of another nature, as the Dulac Problem in dimension three.
publishDate 2002
dc.date.none.fl_str_mv 2002-12-01
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=S0001-37652002000400002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652002000400002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0001-37652002000400002
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.74 n.4 2002
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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