Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points

In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if they are separated by a hyperbola or an ellips...

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Autores: Benterki, Rebiha|||0000-0001-6745-2747, Llibre, Jaume|||0000-0002-9511-5999
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:228103
Acesso em linha:https://ddd.uab.cat/record/228103
https://dx.doi.org/urn:doi:10.3390/MATH8050755
Access Level:acceso abierto
Palavra-chave:Piecewise smooth vector field
Hamiltonian system
Crossing limit cycles
Conics
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spelling Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium pointsBenterki, Rebiha|||0000-0001-6745-2747Llibre, Jaume|||0000-0002-9511-5999Piecewise smooth vector fieldHamiltonian systemCrossing limit cyclesConicsIn this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if they are separated by a hyperbola or an ellipse, they can have at most three crossing limit cycles. Additionally, we prove that these upper bounds are reached. Secondly, we show that there is an example of two crossing limit cycles when these systems have four zones separated by three straight lines. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/228103https://dx.doi.org/urn:doi:10.3390/MATH8050755reponame: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 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:2281032026-06-06T12:50:31Z
dc.title.none.fl_str_mv Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
title Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
spellingShingle Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
Benterki, Rebiha|||0000-0001-6745-2747
Piecewise smooth vector field
Hamiltonian system
Crossing limit cycles
Conics
title_short Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
title_full Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
title_fullStr Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
title_full_unstemmed Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
title_sort Crossing limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points
dc.creator.none.fl_str_mv Benterki, Rebiha|||0000-0001-6745-2747
Llibre, Jaume|||0000-0002-9511-5999
author Benterki, Rebiha|||0000-0001-6745-2747
author_facet Benterki, Rebiha|||0000-0001-6745-2747
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Piecewise smooth vector field
Hamiltonian system
Crossing limit cycles
Conics
topic Piecewise smooth vector field
Hamiltonian system
Crossing limit cycles
Conics
description In this paper, we study the existence of limit cycles of planar piecewise linear Hamiltonian systems without equilibrium points. Firstly, we prove that if these systems are separated by a parabola, they can have at most two crossing limit cycles, and if they are separated by a hyperbola or an ellipse, they can have at most three crossing limit cycles. Additionally, we prove that these upper bounds are reached. Secondly, we show that there is an example of two crossing limit cycles when these systems have four zones separated by three straight lines.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
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/228103
https://dx.doi.org/urn:doi:10.3390/MATH8050755
url https://ddd.uab.cat/record/228103
https://dx.doi.org/urn:doi:10.3390/MATH8050755
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://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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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