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

Given a C∞ family of planar vector fields{Xˆ µ}ˆ µ∈ ˆ W having a hyperbolic saddle, we study the Dulac map D(s; ˆ µ) and the Dulac time T(s; ˆ µ) between two transverse sections located in these paratrices at arbitrary distance from the saddle. We show (Theorems A and B, respectively) that, for any...

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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:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:236661
Acceso en línea:https://ddd.uab.cat/record/236661
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.11.020
Access Level:acceso abierto
Palabra clave:Dulac map
Dulac time
Asymptotic expansion
Uniform flatness
Criticality
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spelling Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddlesGeneral settingMarín, David|||0000-0003-4422-6418Villadelprat Yagüe, Jordi|||0000-0002-1168-9750Dulac mapDulac timeAsymptotic expansionUniform flatnessCriticalityGiven a C∞ family of planar vector fields{Xˆ µ}ˆ µ∈ ˆ W having a hyperbolic saddle, we study the Dulac map D(s; ˆ µ) and the Dulac time T(s; ˆ µ) between two transverse sections located in these paratrices at arbitrary distance from the saddle. We show (Theorems A and B, respectively) that, for any ˆ µ0 ∈ ˆ W and L. 22021-01-0120212021-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/236661https://dx.doi.org/urn:doi:10.1016/j.jde.2020.11.020reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgència 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-2014-0445Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1725Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-095998-B-I00Ministerio 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-Popen 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:2366612026-06-06T12:50:31Z
dc.title.none.fl_str_mv Asymptotic expansion of the Dulac map and time for unfoldings of hyperbolic saddles
General 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
Criticality
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
Criticality
topic Dulac map
Dulac time
Asymptotic expansion
Uniform flatness
Criticality
description Given a C∞ family of planar vector fields{Xˆ µ}ˆ µ∈ ˆ W having a hyperbolic saddle, we study the Dulac map D(s; ˆ µ) and the Dulac time T(s; ˆ µ) between two transverse sections located in these paratrices at arbitrary distance from the saddle. We show (Theorems A and B, respectively) that, for any ˆ µ0 ∈ ˆ W and L.
publishDate 2021
dc.date.none.fl_str_mv 2
2021-01-01
2021
2021-01-01
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/236661
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.11.020
url https://ddd.uab.cat/record/236661
https://dx.doi.org/urn:doi:10.1016/j.jde.2020.11.020
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv 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
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1725
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-095998-B-I00
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
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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