Generalized analytic integrability of a class of polynomial differential systems in C2

This paper study the type of integrability of differential systems with separable variables x˙=h(x)f(y), y˙ = g(y), where h, f and g are polynomials. We provide a criterion for the existence of generalized analytic first integrals of such differential systems. Moreover we characterize the polynomial...

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Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Tian, Yuzhou|||0000-0002-7624-4971
Formato: artículo
Fecha de publicación:2021
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:257125
Acesso em linha:https://ddd.uab.cat/record/257125
https://dx.doi.org/urn:doi:10.1007/s10440-021-00407-4
Access Level:acceso abierto
Palavra-chave:Polynomial systems
Generalized analytic integrability
Polynomial first integrals
Residue
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spelling Generalized analytic integrability of a class of polynomial differential systems in C2Llibre, Jaume|||0000-0002-9511-5999Tian, Yuzhou|||0000-0002-7624-4971Polynomial systemsGeneralized analytic integrabilityPolynomial first integralsResidueThis paper study the type of integrability of differential systems with separable variables x˙=h(x)f(y), y˙ = g(y), where h, f and g are polynomials. We provide a criterion for the existence of generalized analytic first integrals of such differential systems. Moreover we characterize the polynomial integrability of all such systems. In the particular case h(x) = (ax+ b) we provide necessary and sufficient conditions in order that this subclass of systems has a generalized analytic first integral. These results extend known results from Giné et al. (Discrete Contin. Dyn. Syst. 33:4531-4547, 2013) and Llibre and Valls (Discrete Contin. Dyn. Syst., Ser. B 20:2657-2661, 2015). Such differential systems of separable variables are important due to the fact that after a blow-up change of variables any planar quasi-homogeneous polynomial differential system can be transformed into a special differential system of separable variables x˙ = xf(y), y˙ = g(y), with f and g polynomials. 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/257125https://dx.doi.org/urn:doi:10.1007/s10440-021-00407-4reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2016-77278-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617European Commission https://doi.org/10.13039/501100000780 777911open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2571252026-06-06T12:50:31Z
dc.title.none.fl_str_mv Generalized analytic integrability of a class of polynomial differential systems in C2
title Generalized analytic integrability of a class of polynomial differential systems in C2
spellingShingle Generalized analytic integrability of a class of polynomial differential systems in C2
Llibre, Jaume|||0000-0002-9511-5999
Polynomial systems
Generalized analytic integrability
Polynomial first integrals
Residue
title_short Generalized analytic integrability of a class of polynomial differential systems in C2
title_full Generalized analytic integrability of a class of polynomial differential systems in C2
title_fullStr Generalized analytic integrability of a class of polynomial differential systems in C2
title_full_unstemmed Generalized analytic integrability of a class of polynomial differential systems in C2
title_sort Generalized analytic integrability of a class of polynomial differential systems in C2
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Tian, Yuzhou|||0000-0002-7624-4971
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Tian, Yuzhou|||0000-0002-7624-4971
author_role author
author2 Tian, Yuzhou|||0000-0002-7624-4971
author2_role author
dc.subject.none.fl_str_mv Polynomial systems
Generalized analytic integrability
Polynomial first integrals
Residue
topic Polynomial systems
Generalized analytic integrability
Polynomial first integrals
Residue
description This paper study the type of integrability of differential systems with separable variables x˙=h(x)f(y), y˙ = g(y), where h, f and g are polynomials. We provide a criterion for the existence of generalized analytic first integrals of such differential systems. Moreover we characterize the polynomial integrability of all such systems. In the particular case h(x) = (ax+ b) we provide necessary and sufficient conditions in order that this subclass of systems has a generalized analytic first integral. These results extend known results from Giné et al. (Discrete Contin. Dyn. Syst. 33:4531-4547, 2013) and Llibre and Valls (Discrete Contin. Dyn. Syst., Ser. B 20:2657-2661, 2015). Such differential systems of separable variables are important due to the fact that after a blow-up change of variables any planar quasi-homogeneous polynomial differential system can be transformed into a special differential system of separable variables x˙ = xf(y), y˙ = g(y), with f and g polynomials.
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/257125
https://dx.doi.org/urn:doi:10.1007/s10440-021-00407-4
url https://ddd.uab.cat/record/257125
https://dx.doi.org/urn:doi:10.1007/s10440-021-00407-4
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2016-77278-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
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://rightsstatements.org/vocab/InC/1.0/
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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