Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclin...

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Detalles Bibliográficos
Autores: Lázaro Ochoa, José Tomás|||0000-0003-4395-9708, Delshams Valdés, Amadeu|||0000-0003-4134-8882, Gonchenko, Marina, Gonchenko, Sergey
Tipo de recurso: artículo
Fecha de publicación:2018
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:2117/121505
Acceso en línea:https://hdl.handle.net/2117/121505
https://dx.doi.org/10.3934/dcds.2018196
Access Level:acceso abierto
Palabra clave:Dynamics
Differential equations
Newhouse phenomenon
homoclinic and heteroclinic tangencies
reversible mixed dynamics.
Sistemes dinàmics
Equacions diferencials
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangenciesLázaro Ochoa, José Tomás|||0000-0003-4395-9708Delshams Valdés, Amadeu|||0000-0003-4134-8882Gonchenko, MarinaGonchenko, SergeyDynamicsDifferential equationsNewhouse phenomenonhomoclinic and heteroclinic tangenciesreversible mixed dynamics.Sistemes dinàmicsEquacions diferencialsClassificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theoryClassificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spacesÀrees temàtiques de la UPC::Matemàtiques i estadísticaWe study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations related to the birth of asymptotically stable, unstable and elliptic periodic orbits.Peer ReviewedAmerican Institute of Mathematical Sciences20182018-09-0120182018-09-26journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/121505https://dx.doi.org/10.3934/dcds.2018196reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1215052026-05-27T15:37:01Z
dc.title.none.fl_str_mv Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
title Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
spellingShingle Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
Lázaro Ochoa, José Tomás|||0000-0003-4395-9708
Dynamics
Differential equations
Newhouse phenomenon
homoclinic and heteroclinic tangencies
reversible mixed dynamics.
Sistemes dinàmics
Equacions diferencials
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
title_full Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
title_fullStr Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
title_full_unstemmed Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
title_sort Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies
dc.creator.none.fl_str_mv Lázaro Ochoa, José Tomás|||0000-0003-4395-9708
Delshams Valdés, Amadeu|||0000-0003-4134-8882
Gonchenko, Marina
Gonchenko, Sergey
author Lázaro Ochoa, José Tomás|||0000-0003-4395-9708
author_facet Lázaro Ochoa, José Tomás|||0000-0003-4395-9708
Delshams Valdés, Amadeu|||0000-0003-4134-8882
Gonchenko, Marina
Gonchenko, Sergey
author_role author
author2 Delshams Valdés, Amadeu|||0000-0003-4134-8882
Gonchenko, Marina
Gonchenko, Sergey
author2_role author
author
author
dc.subject.none.fl_str_mv Dynamics
Differential equations
Newhouse phenomenon
homoclinic and heteroclinic tangencies
reversible mixed dynamics.
Sistemes dinàmics
Equacions diferencials
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Dynamics
Differential equations
Newhouse phenomenon
homoclinic and heteroclinic tangencies
reversible mixed dynamics.
Sistemes dinàmics
Equacions diferencials
Classificació AMS::37 Dynamical systems and ergodic theory::37G Local and nonlocal bifurcation theory
Classificació AMS::34 Ordinary differential equations::34G Differential equations in abstract spaces
Àrees temàtiques de la UPC::Matemàtiques i estadística
description We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider one-parameter families of reversible maps unfolding the initial homoclinic tangency and prove the existence of infinitely many sequences (cascades) of bifurcations related to the birth of asymptotically stable, unstable and elliptic periodic orbits.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-09-01
2018
2018-09-26
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/2117/121505
https://dx.doi.org/10.3934/dcds.2018196
url https://hdl.handle.net/2117/121505
https://dx.doi.org/10.3934/dcds.2018196
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
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 15.300724

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