On groups of formal diffeomorphisms of several complex variables
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | |
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=S0001-37652012000400002 |
Resumo: | In this note we announce some results in the study of groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the holonomy group notion of a foliation's leaf. For dimension one, there is a well-established dictionary relating analytic/formal classification of the group, with its algebraic properties (finiteness, commutativity, solvability, among others). Such system of equivalences also characterizes the existence of suitable integrating factors, i.e., invariant vector fields and one-forms associated to the group. Our aim is to state the basic lines of such dictionary for the case of several complex variables groups. Our results are applicable in the construction of suitable integrating factors for holomorphic foliations with singularities. We believe they are a starting point in the study of the connection between Liouvillian integration and transverse structures of holomorphic foliations with singularities in the case of arbitrary codimension. The results in this note are derived from the PhD thesis "Grupos de germes de difeomorfismos complexos em várias variáveis e formas diferenciais" of the first named author (Martelo 2010). |
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On groups of formal diffeomorphisms of several complex variablesFormal complex diffeomorphisminfinitesimal generatorholomorphic foliationgerm of complex diffeomorphismIn this note we announce some results in the study of groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the holonomy group notion of a foliation's leaf. For dimension one, there is a well-established dictionary relating analytic/formal classification of the group, with its algebraic properties (finiteness, commutativity, solvability, among others). Such system of equivalences also characterizes the existence of suitable integrating factors, i.e., invariant vector fields and one-forms associated to the group. Our aim is to state the basic lines of such dictionary for the case of several complex variables groups. Our results are applicable in the construction of suitable integrating factors for holomorphic foliations with singularities. We believe they are a starting point in the study of the connection between Liouvillian integration and transverse structures of holomorphic foliations with singularities in the case of arbitrary codimension. The results in this note are derived from the PhD thesis "Grupos de germes de difeomorfismos complexos em várias variáveis e formas diferenciais" of the first named author (Martelo 2010).Academia Brasileira de Ciências2012-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652012000400002Anais da Academia Brasileira de Ciências v.84 n.4 2012reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/S0001-37652012000400002info:eu-repo/semantics/openAccessMartelo,MitchaelScárdua,Brunoeng2012-11-29T00:00:00Zoai:scielo:S0001-37652012000400002Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2012-11-29T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false |
dc.title.none.fl_str_mv |
On groups of formal diffeomorphisms of several complex variables |
title |
On groups of formal diffeomorphisms of several complex variables |
spellingShingle |
On groups of formal diffeomorphisms of several complex variables Martelo,Mitchael Formal complex diffeomorphism infinitesimal generator holomorphic foliation germ of complex diffeomorphism |
title_short |
On groups of formal diffeomorphisms of several complex variables |
title_full |
On groups of formal diffeomorphisms of several complex variables |
title_fullStr |
On groups of formal diffeomorphisms of several complex variables |
title_full_unstemmed |
On groups of formal diffeomorphisms of several complex variables |
title_sort |
On groups of formal diffeomorphisms of several complex variables |
author |
Martelo,Mitchael |
author_facet |
Martelo,Mitchael Scárdua,Bruno |
author_role |
author |
author2 |
Scárdua,Bruno |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Martelo,Mitchael Scárdua,Bruno |
dc.subject.por.fl_str_mv |
Formal complex diffeomorphism infinitesimal generator holomorphic foliation germ of complex diffeomorphism |
topic |
Formal complex diffeomorphism infinitesimal generator holomorphic foliation germ of complex diffeomorphism |
description |
In this note we announce some results in the study of groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the holonomy group notion of a foliation's leaf. For dimension one, there is a well-established dictionary relating analytic/formal classification of the group, with its algebraic properties (finiteness, commutativity, solvability, among others). Such system of equivalences also characterizes the existence of suitable integrating factors, i.e., invariant vector fields and one-forms associated to the group. Our aim is to state the basic lines of such dictionary for the case of several complex variables groups. Our results are applicable in the construction of suitable integrating factors for holomorphic foliations with singularities. We believe they are a starting point in the study of the connection between Liouvillian integration and transverse structures of holomorphic foliations with singularities in the case of arbitrary codimension. The results in this note are derived from the PhD thesis "Grupos de germes de difeomorfismos complexos em várias variáveis e formas diferenciais" of the first named author (Martelo 2010). |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-12-01 |
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=S0001-37652012000400002 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652012000400002 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S0001-37652012000400002 |
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.84 n.4 2012 reponame:Anais da Academia Brasileira de Ciências (Online) instname:Academia Brasileira de Ciências (ABC) instacron:ABC |
instname_str |
Academia Brasileira de Ciências (ABC) |
instacron_str |
ABC |
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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1754302858751115264 |