Invariant algebraic curves for certain generalized Liénard differential system

In this work we solve the problem of finding the invariant algebraic curves of a generalized Li´enard differential system ˙x = y, ˙y = −f(x)y − g(x), where deg f = m and deg g = n and with n = m + 1, generalizing the known previous examples. In particular it is studied the case m = 3 and n = 4. The...

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Detalles Bibliográficos
Autor: Giné, Jaume
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2023
País:España
Institución:Universitat de Lleida (UdL)
Repositorio:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/464749
Acceso en línea:https://doi.org/10.3934/cpaa.2022159
https://hdl.handle.net/10459.1/464749
Access Level:acceso abierto
Palabra clave:Liénard systems
Invariant algebraic curves
Darboux polynomials
Puiseux series
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spelling Invariant algebraic curves for certain generalized Liénard differential systemGiné, JaumeLiénard systemsInvariant algebraic curvesDarboux polynomialsPuiseux seriesIn this work we solve the problem of finding the invariant algebraic curves of a generalized Li´enard differential system ˙x = y, ˙y = −f(x)y − g(x), where deg f = m and deg g = n and with n = m + 1, generalizing the known previous examples. In particular it is studied the case m = 3 and n = 4. The difficulties in applying the Puiseux method are shown even when the degrees of the invariant curves are bounded.The author is partially supported by the Agencia Estatal de Investigaci´on grant PID2020-113758GB-I00 and an AGAUR (Generalitat de Catalunya) grant number 2017SGR 1276.American Institute of Mathematical Sciences2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionhttps://doi.org/10.3934/cpaa.2022159https://hdl.handle.net/10459.1/464749reponame:Repositori Obert UdL instname:Universitat de Lleida (UdL)Inglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00Versió postprint del document publicat a https://doi.org/10.3934/cpaa.2022159Communications on Pure and Applied Analysis, 2023, vol. 22, núm. 2, p. 480-487(c) American Institute of Mathematical Sciences, 2023info:eu-repo/semantics/openAccessoai:repositori.udl.cat:10459.1/4647492026-06-24T12:42:17Z
dc.title.none.fl_str_mv Invariant algebraic curves for certain generalized Liénard differential system
title Invariant algebraic curves for certain generalized Liénard differential system
spellingShingle Invariant algebraic curves for certain generalized Liénard differential system
Giné, Jaume
Liénard systems
Invariant algebraic curves
Darboux polynomials
Puiseux series
title_short Invariant algebraic curves for certain generalized Liénard differential system
title_full Invariant algebraic curves for certain generalized Liénard differential system
title_fullStr Invariant algebraic curves for certain generalized Liénard differential system
title_full_unstemmed Invariant algebraic curves for certain generalized Liénard differential system
title_sort Invariant algebraic curves for certain generalized Liénard differential system
dc.creator.none.fl_str_mv Giné, Jaume
author Giné, Jaume
author_facet Giné, Jaume
author_role author
dc.subject.none.fl_str_mv Liénard systems
Invariant algebraic curves
Darboux polynomials
Puiseux series
topic Liénard systems
Invariant algebraic curves
Darboux polynomials
Puiseux series
description In this work we solve the problem of finding the invariant algebraic curves of a generalized Li´enard differential system ˙x = y, ˙y = −f(x)y − g(x), where deg f = m and deg g = n and with n = m + 1, generalizing the known previous examples. In particular it is studied the case m = 3 and n = 4. The difficulties in applying the Puiseux method are shown even when the degrees of the invariant curves are bounded.
publishDate 2023
dc.date.none.fl_str_mv 2023
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/10.3934/cpaa.2022159
https://hdl.handle.net/10459.1/464749
url https://doi.org/10.3934/cpaa.2022159
https://hdl.handle.net/10459.1/464749
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113758GB-I00
Versió postprint del document publicat a https://doi.org/10.3934/cpaa.2022159
Communications on Pure and Applied Analysis, 2023, vol. 22, núm. 2, p. 480-487
dc.rights.none.fl_str_mv (c) American Institute of Mathematical Sciences, 2023
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) American Institute of Mathematical Sciences, 2023
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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