Formal inverse integrating factors and the nilpotent center problem

We are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to characterize such a centers we use a more general object, namely, formal inverse inte...

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Detalles Bibliográficos
Autor: García, I. A. (Isaac A.)
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2016
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/58362
Acceso en línea:https://doi.org/10.1142/S0218127416500152
http://hdl.handle.net/10459.1/58362
Access Level:acceso abierto
Palabra clave:Monodromic singularity
Nilpotent center
Integrability
Inverse integrating factor
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spelling Formal inverse integrating factors and the nilpotent center problemGarcía, I. A. (Isaac A.)Monodromic singularityNilpotent centerIntegrabilityInverse integrating factorWe are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to characterize such a centers we use a more general object, namely, formal inverse integrating factors V of X. Although by the existence of V is not possible to describe all nilpotent centers strata, we simplify, improve and also extend previous results on the relationship between these concepts. We use in the performed analysis the so-called Andreev number n N with n > 2 associated to X which is invariant under orbital conjugacy of X. Besides the leading terms in the (1,n)-quasihomogeneous expansions that V can have we also prove the following: (i) If n is even and there exists V then X has a center; (iii) If the existence of V characterizes all the centers; (iii) If there is a V with minimum ``vanishing multiplicity' at the singularity then, generically, X has a center.The author is partially supported by a MINECO grant number MTM2014-53703-P and by a CIRIT grant number 2014 SGR 1204.World Scientific Publishing2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://doi.org/10.1142/S0218127416500152http://hdl.handle.net/10459.1/58362reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/MINECO//MTM2014-53703-PVersió postprint del document publicat a https://doi.org/10.1142/S0218127416500152International Journal of Bifurcation and Chaos, 2016, vol. 26, p. 1650015-1-1650015-13(c) World Scientific Publishing, 2016info:eu-repo/semantics/openAccessoai:repositori.udl.cat:10459.1/583622026-06-24T12:42:17Z
dc.title.none.fl_str_mv Formal inverse integrating factors and the nilpotent center problem
title Formal inverse integrating factors and the nilpotent center problem
spellingShingle Formal inverse integrating factors and the nilpotent center problem
García, I. A. (Isaac A.)
Monodromic singularity
Nilpotent center
Integrability
Inverse integrating factor
title_short Formal inverse integrating factors and the nilpotent center problem
title_full Formal inverse integrating factors and the nilpotent center problem
title_fullStr Formal inverse integrating factors and the nilpotent center problem
title_full_unstemmed Formal inverse integrating factors and the nilpotent center problem
title_sort Formal inverse integrating factors and the nilpotent center problem
dc.creator.none.fl_str_mv García, I. A. (Isaac A.)
author García, I. A. (Isaac A.)
author_facet García, I. A. (Isaac A.)
author_role author
dc.subject.none.fl_str_mv Monodromic singularity
Nilpotent center
Integrability
Inverse integrating factor
topic Monodromic singularity
Nilpotent center
Integrability
Inverse integrating factor
description We are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to characterize such a centers we use a more general object, namely, formal inverse integrating factors V of X. Although by the existence of V is not possible to describe all nilpotent centers strata, we simplify, improve and also extend previous results on the relationship between these concepts. We use in the performed analysis the so-called Andreev number n N with n > 2 associated to X which is invariant under orbital conjugacy of X. Besides the leading terms in the (1,n)-quasihomogeneous expansions that V can have we also prove the following: (i) If n is even and there exists V then X has a center; (iii) If the existence of V characterizes all the centers; (iii) If there is a V with minimum ``vanishing multiplicity' at the singularity then, generically, X has a center.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://doi.org/10.1142/S0218127416500152
http://hdl.handle.net/10459.1/58362
url https://doi.org/10.1142/S0218127416500152
http://hdl.handle.net/10459.1/58362
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MINECO//MTM2014-53703-P
Versió postprint del document publicat a https://doi.org/10.1142/S0218127416500152
International Journal of Bifurcation and Chaos, 2016, vol. 26, p. 1650015-1-1650015-13
dc.rights.none.fl_str_mv (c) World Scientific Publishing, 2016
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) World Scientific Publishing, 2016
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv World Scientific Publishing
publisher.none.fl_str_mv World Scientific Publishing
dc.source.none.fl_str_mv reponame:Repositori Obert UdL
instname:Universitat de Lleida (UdL)
instname_str Universitat de Lleida (UdL)
reponame_str Repositori Obert UdL
collection Repositori Obert UdL
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repository.mail.fl_str_mv
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