Discrete Melnikov functions

We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented.) having when (Formula presented.) an open continuum of initial conditions such that the corresponding sequences are N-periodic. From the study of some variational equations of low order, we obtain succes...

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Autores: Gasull, Armengol|||0000-0002-1719-8231, 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:257089
Acceso en línea:https://ddd.uab.cat/record/257089
https://dx.doi.org/urn:doi:10.1080/10236198.2021.1970147
Access Level:acceso abierto
Palabra clave:Discrete non-autonomous dynamical systems
Periodic sequences
Melnikov functions
Difference equations
Bifurcation
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spelling Discrete Melnikov functionsGasull, Armengol|||0000-0002-1719-8231Valls, Clàudia|||0000-0001-8279-1229Discrete non-autonomous dynamical systemsPeriodic sequencesMelnikov functionsDifference equationsBifurcationWe consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented.) having when (Formula presented.) an open continuum of initial conditions such that the corresponding sequences are N-periodic. From the study of some variational equations of low order, we obtain successive maps, that we call discrete Melnikov functions, such that the simple zeroes of the first one that is not identically zero control the initial conditions that persist as N-periodic sequences of the perturbed discrete dynamical system. We apply these results to several examples, including some Abel-type discrete dynamical systems and some non-autonomous perturbed globally periodic difference equations. 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/257089https://dx.doi.org/urn:doi:10.1080/10236198.2021.1970147reponame: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-1617open accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2570892026-06-06T12:50:31Z
dc.title.none.fl_str_mv Discrete Melnikov functions
title Discrete Melnikov functions
spellingShingle Discrete Melnikov functions
Gasull, Armengol|||0000-0002-1719-8231
Discrete non-autonomous dynamical systems
Periodic sequences
Melnikov functions
Difference equations
Bifurcation
title_short Discrete Melnikov functions
title_full Discrete Melnikov functions
title_fullStr Discrete Melnikov functions
title_full_unstemmed Discrete Melnikov functions
title_sort Discrete Melnikov functions
dc.creator.none.fl_str_mv Gasull, Armengol|||0000-0002-1719-8231
Valls, Clàudia|||0000-0001-8279-1229
author Gasull, Armengol|||0000-0002-1719-8231
author_facet Gasull, Armengol|||0000-0002-1719-8231
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 Discrete non-autonomous dynamical systems
Periodic sequences
Melnikov functions
Difference equations
Bifurcation
topic Discrete non-autonomous dynamical systems
Periodic sequences
Melnikov functions
Difference equations
Bifurcation
description We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented.) having when (Formula presented.) an open continuum of initial conditions such that the corresponding sequences are N-periodic. From the study of some variational equations of low order, we obtain successive maps, that we call discrete Melnikov functions, such that the simple zeroes of the first one that is not identically zero control the initial conditions that persist as N-periodic sequences of the perturbed discrete dynamical system. We apply these results to several examples, including some Abel-type discrete dynamical systems and some non-autonomous perturbed globally periodic difference equations.
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
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dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/257089
https://dx.doi.org/urn:doi:10.1080/10236198.2021.1970147
url https://ddd.uab.cat/record/257089
https://dx.doi.org/urn:doi:10.1080/10236198.2021.1970147
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
dc.rights.none.fl_str_mv open access
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dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
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eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
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