Floquet theory for second order linear homogeneous difference equations

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Difference Equations and Applications on 05/11/2015, available online: http://www.tandfonline.com/10.1080/10236198.2015.1100609

Detalles Bibliográficos
Autores: Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373, Jiménez Jiménez, María José|||0000-0003-3502-462X
Tipo de recurso: artículo
Fecha de publicación:2015
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:2117/80510
Acceso en línea:https://hdl.handle.net/2117/80510
https://dx.doi.org/10.1080/10236198.2015.1100609
Access Level:acceso abierto
Palabra clave:Floquet theory
Difference equations
Periodic sequences
Chebyshev polynomials
Equacions en diferències
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::11 Number theory::11B Sequences and sets
Classificació AMS::33 Special functions::33C Hypergeometric functions
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
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spelling Floquet theory for second order linear homogeneous difference equationsEncinas Bachiller, Andrés Marcos|||0000-0001-5588-0373Jiménez Jiménez, María José|||0000-0003-3502-462XFloquet theoryDifference equationsDifference equationsFloquet theoryPeriodic sequencesChebyshev polynomialsEquacions en diferènciesClassificació AMS::39 Difference and functional equations::39A Difference equationsClassificació AMS::11 Number theory::11B Sequences and setsClassificació AMS::33 Special functions::33C Hypergeometric functionsÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferènciesThis is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Difference Equations and Applications on 05/11/2015, available online: http://www.tandfonline.com/10.1080/10236198.2015.1100609In this paper we provide a version of the Floquet’s theorem to be applied to any second order difference equations with quasi-periodic coefficients. To do this we extend to second order linear difference equations with quasi-periodic coefficients, the known equivalence between the Chebyshev equations and the second order linear difference equations with constant coefficients. So, any second order linear difference equations with quasi-periodic coefficients is essentially equivalent to a Chebyshev equation, whose parameter only depends on the values of the quasi-periodic coefficients and can be determined by a non-linear recurrence. Moreover, we solve this recurrence and obtaining a closed expression for this parameter. As a by-product we also obtain a Floquet’s type result; that is, the necessary and sufficient condition for the equation has quasi-periodic solutions.Peer Reviewed20152015-11-0520152015-12-15journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/80510https://dx.doi.org/10.1080/10236198.2015.1100609reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2014-60450-R LA RESISTENCIA EFECTIVA COMO HERRAMIENTA PARA EL ESTUDIO DEL PROBLEMA INVERSO DE LAS CONDUCTANCIAS Y EL ANALISIS DE LAS PERTURBACIONES DE REDESopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/805102026-05-27T15:37:01Z
dc.title.none.fl_str_mv Floquet theory for second order linear homogeneous difference equations
title Floquet theory for second order linear homogeneous difference equations
spellingShingle Floquet theory for second order linear homogeneous difference equations
Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Floquet theory
Difference equations
Difference equations
Floquet theory
Periodic sequences
Chebyshev polynomials
Equacions en diferències
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::11 Number theory::11B Sequences and sets
Classificació AMS::33 Special functions::33C Hypergeometric functions
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
title_short Floquet theory for second order linear homogeneous difference equations
title_full Floquet theory for second order linear homogeneous difference equations
title_fullStr Floquet theory for second order linear homogeneous difference equations
title_full_unstemmed Floquet theory for second order linear homogeneous difference equations
title_sort Floquet theory for second order linear homogeneous difference equations
dc.creator.none.fl_str_mv Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Jiménez Jiménez, María José|||0000-0003-3502-462X
author Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
author_facet Encinas Bachiller, Andrés Marcos|||0000-0001-5588-0373
Jiménez Jiménez, María José|||0000-0003-3502-462X
author_role author
author2 Jiménez Jiménez, María José|||0000-0003-3502-462X
author2_role author
dc.subject.none.fl_str_mv Floquet theory
Difference equations
Difference equations
Floquet theory
Periodic sequences
Chebyshev polynomials
Equacions en diferències
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::11 Number theory::11B Sequences and sets
Classificació AMS::33 Special functions::33C Hypergeometric functions
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
topic Floquet theory
Difference equations
Difference equations
Floquet theory
Periodic sequences
Chebyshev polynomials
Equacions en diferències
Classificació AMS::39 Difference and functional equations::39A Difference equations
Classificació AMS::11 Number theory::11B Sequences and sets
Classificació AMS::33 Special functions::33C Hypergeometric functions
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en diferències
description This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Difference Equations and Applications on 05/11/2015, available online: http://www.tandfonline.com/10.1080/10236198.2015.1100609
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-11-05
2015
2015-12-15
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/2117/80510
https://dx.doi.org/10.1080/10236198.2015.1100609
url https://hdl.handle.net/2117/80510
https://dx.doi.org/10.1080/10236198.2015.1100609
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2014-60450-R LA RESISTENCIA EFECTIVA COMO HERRAMIENTA PARA EL ESTUDIO DEL PROBLEMA INVERSO DE LAS CONDUCTANCIAS Y EL ANALISIS DE LAS PERTURBACIONES DE REDES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

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

http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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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