Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres

We study the continuous and discontinuous planar piecewise differential systems formed by linear centres together with linear Hamiltonian saddles separated by one or two parallel straight lines. When these piecewise differential systems are either continuous or discontinuous separated by one straigh...

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Autores: Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:267128
Acceso en línea:https://ddd.uab.cat/record/267128
https://dx.doi.org/urn:doi:10.1080/14689367.2022.2037519
Access Level:acceso abierto
Palabra clave:Limit cycles
Linear centers
Linear Hamiltonian saddles
Continuous piecewise linear differential systems
Discontinuous piecewise differential systems
First integrals
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spelling Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centresLlibre, Jaume|||0000-0002-9511-5999Valls, Clàudia|||0000-0001-8279-1229Limit cyclesLinear centersLinear Hamiltonian saddlesContinuous piecewise linear differential systemsDiscontinuous piecewise differential systemsFirst integralsWe study the continuous and discontinuous planar piecewise differential systems formed by linear centres together with linear Hamiltonian saddles separated by one or two parallel straight lines. When these piecewise differential systems are either continuous or discontinuous separated by one straight line, they have no limit cycles. When these piecewise differential systems are continuous and are separated by two parallel straight lines they do not have limit cycles. On the other hand, when these piecewise differential systems are discontinuous and separated by two parallel straight lines (either two centres and one saddle, or two saddles and one centre), we show that they can have at most one limit cycle, and that there exist such systems with one limit cycle. If the piecewise differential systems separated by two parallel straight lines have three linear centres or three linear Hamiltonian saddles it is known that they have at most one limit cycle. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/267128https://dx.doi.org/urn:doi:10.1080/14689367.2022.2037519reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00Agència 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 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, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2671282026-06-06T12:50:31Z
dc.title.none.fl_str_mv Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
title Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
spellingShingle Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
Llibre, Jaume|||0000-0002-9511-5999
Limit cycles
Linear centers
Linear Hamiltonian saddles
Continuous piecewise linear differential systems
Discontinuous piecewise differential systems
First integrals
title_short Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
title_full Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
title_fullStr Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
title_full_unstemmed Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
title_sort Limit cycles of piecewise differential systems with linear Hamiltonian saddles and linear centres
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Valls, Clàudia|||0000-0001-8279-1229
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Valls, Clàudia|||0000-0001-8279-1229
author_role author
author2 Valls, Clàudia|||0000-0001-8279-1229
author2_role author
dc.subject.none.fl_str_mv Limit cycles
Linear centers
Linear Hamiltonian saddles
Continuous piecewise linear differential systems
Discontinuous piecewise differential systems
First integrals
topic Limit cycles
Linear centers
Linear Hamiltonian saddles
Continuous piecewise linear differential systems
Discontinuous piecewise differential systems
First integrals
description We study the continuous and discontinuous planar piecewise differential systems formed by linear centres together with linear Hamiltonian saddles separated by one or two parallel straight lines. When these piecewise differential systems are either continuous or discontinuous separated by one straight line, they have no limit cycles. When these piecewise differential systems are continuous and are separated by two parallel straight lines they do not have limit cycles. On the other hand, when these piecewise differential systems are discontinuous and separated by two parallel straight lines (either two centres and one saddle, or two saddles and one centre), we show that they can have at most one limit cycle, and that there exist such systems with one limit cycle. If the piecewise differential systems separated by two parallel straight lines have three linear centres or three linear Hamiltonian saddles it is known that they have at most one limit cycle.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
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/267128
https://dx.doi.org/urn:doi:10.1080/14689367.2022.2037519
url https://ddd.uab.cat/record/267128
https://dx.doi.org/urn:doi:10.1080/14689367.2022.2037519
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 PID2019-104658GB-I00
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://creativecommons.org/licenses/by-nc/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/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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