Adiabatic invariant of the harmonic oscillator, complex matching and resurgence

The linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain rigorously the asymptotic variation of the action of the associated hamiltonian...

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Detalles Bibliográficos
Autores: Bonet Revés, Carles|||0000-0002-4413-7952, Sauzin, D., Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717, València Guitart, Marta|||0000-0001-9597-3718
Tipo de recurso: artículo
Fecha de publicación:1997
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:2117/857
Acceso en línea:https://hdl.handle.net/2117/857
Access Level:acceso abierto
Palabra clave:Differential equations
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
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spelling Adiabatic invariant of the harmonic oscillator, complex matching and resurgenceBonet Revés, Carles|||0000-0002-4413-7952Sauzin, D.Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717València Guitart, Marta|||0000-0001-9597-3718Differential equationsEquacions diferencials ordinàriesEquacions diferencials ordinàriesClassificació AMS::34 Ordinary differential equations::34C Qualitative theoryClassificació AMS::34 Ordinary differential equations::34A General theoryClassificació AMS::34 Ordinary differential equations::34E Asymptotic theoryClassificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanicsClassificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamicsThe linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain rigorously the asymptotic variation of the action of the associated hamiltonian beyond all orders. The solution in the complex plane is aproximated by a series in which all terms present a singularity at the same point. Following matching techniques near this singularity one is led to an equation which does not depend on any parameter, the so-called inner equation, of a Riccati type. This equation is studied by resurgence methods.19971997-01-0120072007-05-03journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/857reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 2.5 Spainhttp://creativecommons.org/licenses/by-nc-nd/2.5/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/8572026-05-27T15:37:01Z
dc.title.none.fl_str_mv Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
title Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
spellingShingle Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
Bonet Revés, Carles|||0000-0002-4413-7952
Differential equations
Equacions diferencials ordinàries
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
title_short Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
title_full Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
title_fullStr Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
title_full_unstemmed Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
title_sort Adiabatic invariant of the harmonic oscillator, complex matching and resurgence
dc.creator.none.fl_str_mv Bonet Revés, Carles|||0000-0002-4413-7952
Sauzin, D.
Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717
València Guitart, Marta|||0000-0001-9597-3718
author Bonet Revés, Carles|||0000-0002-4413-7952
author_facet Bonet Revés, Carles|||0000-0002-4413-7952
Sauzin, D.
Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717
València Guitart, Marta|||0000-0001-9597-3718
author_role author
author2 Sauzin, D.
Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717
València Guitart, Marta|||0000-0001-9597-3718
author2_role author
author
author
dc.subject.none.fl_str_mv Differential equations
Equacions diferencials ordinàries
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
topic Differential equations
Equacions diferencials ordinàries
Equacions diferencials ordinàries
Classificació AMS::34 Ordinary differential equations::34C Qualitative theory
Classificació AMS::34 Ordinary differential equations::34A General theory
Classificació AMS::34 Ordinary differential equations::34E Asymptotic theory
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Classificació AMS::70 Mechanics of particles and systems::70K Nonlinear dynamics
description The linear oscillator equation with a frequency depending slowly on time is used to test a method to compute exponentially small quantities. This work present the matching method in the complex plane as a tool to obtain rigorously the asymptotic variation of the action of the associated hamiltonian beyond all orders. The solution in the complex plane is aproximated by a series in which all terms present a singularity at the same point. Following matching techniques near this singularity one is led to an equation which does not depend on any parameter, the so-called inner equation, of a Riccati type. This equation is studied by resurgence methods.
publishDate 1997
dc.date.none.fl_str_mv 1997
1997-01-01
2007
2007-05-03
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/857
url https://hdl.handle.net/2117/857
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 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/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 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/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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score 15,300724

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