Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles

In this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle. We give a structure theorem for the asymptotic expansion of the local Dulac time (as well as the local Dulac map) with the remainder uniformly flat with respect to the unfolding parameters....

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Detalles Bibliográficos
Autores: Marín, David|||0000-0003-4422-6418, Villadelprat Yagüe, Jordi|||0000-0002-1168-9750
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:236669
Acceso en línea:https://ddd.uab.cat/record/236669
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.06.024
Access Level:acceso abierto
Palabra clave:Dulac map
Dulac time
Asymptotic expansion
Uniform flatness
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spelling Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddlesLocal settingMarín, David|||0000-0003-4422-6418Villadelprat Yagüe, Jordi|||0000-0002-1168-9750Dulac mapDulac timeAsymptotic expansionUniform flatnessIn this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle. We give a structure theorem for the asymptotic expansion of the local Dulac time (as well as the local Dulac map) with the remainder uniformly flat with respect to the unfolding parameters. Here local means close enough to the saddle in order that the normalizing coordinates provided by a suitable normal form can be used. The principal part of the asymptotic expansion is given in a monomial scale containing a deformation of the logarithm, the so-called Roussarie-Ecalle compensator. Especial attention is paid to the remainder's properties concerning the derivation with respect to the unfolding parameters. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/236669https://dx.doi.org/urn:doi:10.1016/j.jde.2020.06.024reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2015-66165-PAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-86795-C3-2-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1725Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2366692026-06-06T12:50:31Z
dc.title.none.fl_str_mv Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
Local setting
title Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
spellingShingle Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
Marín, David|||0000-0003-4422-6418
Dulac map
Dulac time
Asymptotic expansion
Uniform flatness
title_short Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
title_full Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
title_fullStr Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
title_full_unstemmed Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
title_sort Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
dc.creator.none.fl_str_mv Marín, David|||0000-0003-4422-6418
Villadelprat Yagüe, Jordi|||0000-0002-1168-9750
author Marín, David|||0000-0003-4422-6418
author_facet Marín, David|||0000-0003-4422-6418
Villadelprat Yagüe, Jordi|||0000-0002-1168-9750
author_role author
author2 Villadelprat Yagüe, Jordi|||0000-0002-1168-9750
author2_role author
dc.subject.none.fl_str_mv Dulac map
Dulac time
Asymptotic expansion
Uniform flatness
topic Dulac map
Dulac time
Asymptotic expansion
Uniform flatness
description In this paper we study unfoldings of planar vector fields in a neighbourhood of a hyperbolic resonant saddle. We give a structure theorem for the asymptotic expansion of the local Dulac time (as well as the local Dulac map) with the remainder uniformly flat with respect to the unfolding parameters. Here local means close enough to the saddle in order that the normalizing coordinates provided by a suitable normal form can be used. The principal part of the asymptotic expansion is given in a monomial scale containing a deformation of the logarithm, the so-called Roussarie-Ecalle compensator. Especial attention is paid to the remainder's properties concerning the derivation with respect to the unfolding parameters.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/236669
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.06.024
url https://ddd.uab.cat/record/236669
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.06.024
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2015-66165-P
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-86795-C3-2-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1725
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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repository.mail.fl_str_mv
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