A Route to chaos in the Boros–Moll map

The Boros–Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros–Moll one, showing that the existence of an unbo...

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Detalles Bibliográficos
Autores: Gardini, Laura, Mañosa Fernández, Víctor|||0000-0002-5082-3334, Sushko, Iryna
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/132567
Acceso en línea:https://hdl.handle.net/2117/132567
https://dx.doi.org/10.1142/S021812741930009X
Access Level:acceso abierto
Palabra clave:Differentiable dynamical systems
Chaotic behavior in systems
Boros–Moll map
chaotic set
critical line
homoclinic bifurcation
noninvertible planar map
snapback repellor
Sistemes dinàmics diferenciables
Caos (Teoria de sistemes)
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
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network_acronym_str ES
network_name_str España
repository_id_str
spelling A Route to chaos in the Boros–Moll mapGardini, LauraMañosa Fernández, Víctor|||0000-0002-5082-3334Sushko, IrynaDifferentiable dynamical systemsChaotic behavior in systemsBoros–Moll mapchaotic setcritical linehomoclinic bifurcationnoninvertible planar mapsnapback repellorSistemes dinàmics diferenciablesCaos (Teoria de sistemes)Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behaviorClassificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theoryÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmicsThe Boros–Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros–Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros–Moll map is a peculiar feature within the family. We relate this singularity with a specific property of the critical lines that occurs only for this special case. In particular, we explain how the unbounded chaotic region in the Boros–Moll map appears. We especially explain the main contact/homoclinic bifurcations that occur in the family. We also report some other bifurcation phenomena that appear in the considered unfolding.Peer Reviewed20192019-04-0120192019-05-03journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/132567https://dx.doi.org/10.1142/S021812741930009Xreponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1325672026-05-27T15:37:01Z
dc.title.none.fl_str_mv A Route to chaos in the Boros–Moll map
title A Route to chaos in the Boros–Moll map
spellingShingle A Route to chaos in the Boros–Moll map
Gardini, Laura
Differentiable dynamical systems
Chaotic behavior in systems
Boros–Moll map
chaotic set
critical line
homoclinic bifurcation
noninvertible planar map
snapback repellor
Sistemes dinàmics diferenciables
Caos (Teoria de sistemes)
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
title_short A Route to chaos in the Boros–Moll map
title_full A Route to chaos in the Boros–Moll map
title_fullStr A Route to chaos in the Boros–Moll map
title_full_unstemmed A Route to chaos in the Boros–Moll map
title_sort A Route to chaos in the Boros–Moll map
dc.creator.none.fl_str_mv Gardini, Laura
Mañosa Fernández, Víctor|||0000-0002-5082-3334
Sushko, Iryna
author Gardini, Laura
author_facet Gardini, Laura
Mañosa Fernández, Víctor|||0000-0002-5082-3334
Sushko, Iryna
author_role author
author2 Mañosa Fernández, Víctor|||0000-0002-5082-3334
Sushko, Iryna
author2_role author
author
dc.subject.none.fl_str_mv Differentiable dynamical systems
Chaotic behavior in systems
Boros–Moll map
chaotic set
critical line
homoclinic bifurcation
noninvertible planar map
snapback repellor
Sistemes dinàmics diferenciables
Caos (Teoria de sistemes)
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
topic Differentiable dynamical systems
Chaotic behavior in systems
Boros–Moll map
chaotic set
critical line
homoclinic bifurcation
noninvertible planar map
snapback repellor
Sistemes dinàmics diferenciables
Caos (Teoria de sistemes)
Classificació AMS::37 Dynamical systems and ergodic theory::37D Dynamical systems with hyperbolic behavior
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
description The Boros–Moll map appears as a subsystem of a Landen transformation associated to certain rational integrals and its dynamics is related to their convergence. In the paper, we study the dynamics of a one-parameter family of maps which unfold the Boros–Moll one, showing that the existence of an unbounded invariant chaotic region in the Boros–Moll map is a peculiar feature within the family. We relate this singularity with a specific property of the critical lines that occurs only for this special case. In particular, we explain how the unbounded chaotic region in the Boros–Moll map appears. We especially explain the main contact/homoclinic bifurcations that occur in the family. We also report some other bifurcation phenomena that appear in the considered unfolding.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-04-01
2019
2019-05-03
dc.type.none.fl_str_mv journal 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://hdl.handle.net/2117/132567
https://dx.doi.org/10.1142/S021812741930009X
url https://hdl.handle.net/2117/132567
https://dx.doi.org/10.1142/S021812741930009X
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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