Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views

The following differential quadratic polynomial differential system dx/dt=y-x, dy/dt=2y-y/y-1(2-yy-5y-4/y-1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of rad...

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Autores: Artés Ferragud, Joan Carles|||0000-0003-4332-7495, Llibre, Jaume|||0000-0002-9511-5999, Vulpe, Nicolae
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:289972
Acceso en línea:https://ddd.uab.cat/record/289972
https://dx.doi.org/urn:doi:10.3390/appliedmath4010004
Access Level:acceso abierto
Palabra clave:Isotropic star
Polynomial differential equation
Phase portrait
Poincaré disc
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spelling Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of ViewsArtés Ferragud, Joan Carles|||0000-0003-4332-7495Llibre, Jaume|||0000-0002-9511-5999Vulpe, NicolaeIsotropic starPolynomial differential equationPhase portraitPoincaré discThe following differential quadratic polynomial differential system dx/dt=y-x, dy/dt=2y-y/y-1(2-yy-5y-4/y-1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. First, we classify all the topologically non-equivalent phase portraits in the Poincaré disc of these quadratic polynomial differential systems for all values of the parameter y∈R∖{1}. Second, using the information of the different phase portraits obtained we classify the possible limit values of m(r)/r and 4πr2ρ of an isotropic star when r decreases. 22024-01-0120242024-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/289972https://dx.doi.org/urn:doi:10.3390/appliedmath4010004reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-I00European Commission https://doi.org/10.13039/501100000780 777911Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113open 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, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2899722026-06-06T12:50:31Z
dc.title.none.fl_str_mv Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
title Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
spellingShingle Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Isotropic star
Polynomial differential equation
Phase portrait
Poincaré disc
title_short Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
title_full Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
title_fullStr Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
title_full_unstemmed Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
title_sort Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
dc.creator.none.fl_str_mv Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Llibre, Jaume|||0000-0002-9511-5999
Vulpe, Nicolae
author Artés Ferragud, Joan Carles|||0000-0003-4332-7495
author_facet Artés Ferragud, Joan Carles|||0000-0003-4332-7495
Llibre, Jaume|||0000-0002-9511-5999
Vulpe, Nicolae
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Vulpe, Nicolae
author2_role author
author
dc.subject.none.fl_str_mv Isotropic star
Polynomial differential equation
Phase portrait
Poincaré disc
topic Isotropic star
Polynomial differential equation
Phase portrait
Poincaré disc
description The following differential quadratic polynomial differential system dx/dt=y-x, dy/dt=2y-y/y-1(2-yy-5y-4/y-1x), when the parameter y∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. First, we classify all the topologically non-equivalent phase portraits in the Poincaré disc of these quadratic polynomial differential systems for all values of the parameter y∈R∖{1}. Second, using the information of the different phase portraits obtained we classify the possible limit values of m(r)/r and 4πr2ρ of an isotropic star when r decreases.
publishDate 2024
dc.date.none.fl_str_mv 2
2024-01-01
2024
2024-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/289972
https://dx.doi.org/urn:doi:10.3390/appliedmath4010004
url https://ddd.uab.cat/record/289972
https://dx.doi.org/urn:doi:10.3390/appliedmath4010004
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2022-136613NB-I00
European Commission https://doi.org/10.13039/501100000780 777911
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2021/SGR-00113
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by/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/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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