How to apply numerical tools to study dynamical systems : The CP problem

Given a system of differential equations, normally it is not possible to find the associated solutions analytically, so other ways have to be taken into account in order to describe the behaviour of the system. The goal of this thesis is to study how to construct numerically the skeleton of a given...

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Detalles Bibliográficos
Autor: Aranda May, Montserrat
Tipo de recurso: tesis de maestría
Fecha de publicación:2014
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:2099.1/23113
Acceso en línea:https://hdl.handle.net/2099.1/23113
Access Level:acceso abierto
Palabra clave:Numerical analysis
Numerical Methods
Dynamical Systems
Hamiltonian Systems
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65P Numerical problems in dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
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spelling How to apply numerical tools to study dynamical systems : The CP problemAranda May, MontserratNumerical analysisNumerical MethodsDynamical SystemsHamiltonian SystemsAnàlisi numèricaClassificació AMS::65 Numerical analysis::65P Numerical problems in dynamical systemsÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèricaGiven a system of differential equations, normally it is not possible to find the associated solutions analytically, so other ways have to be taken into account in order to describe the behaviour of the system. The goal of this thesis is to study how to construct numerically the skeleton of a given dynamical system, starting with the computation of the easiest solutions -equilibrium points- and following with other invariant objects as manifolds of equilibria, homoclinic orbits, periodic orbits (PO), manifolds of PO, chaos, island chains, etc. Thanks to these particular solutions and using well-known theory of Dynamical Systems, one can get an idea of the general behaviour of the system. The project studies the particular case of the system that models the behaviour of a hydrogen atom in a circularly polarized microwave field (CP problem).Universitat Politècnica de CatalunyaOllé Torner, Mercè20142014-07-0120142014-10-17master thesishttp://purl.org/coar/resource_type/c_bdccNAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2099.1/23113reponame: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:2099.1/231132026-05-27T15:37:01Z
dc.title.none.fl_str_mv How to apply numerical tools to study dynamical systems : The CP problem
title How to apply numerical tools to study dynamical systems : The CP problem
spellingShingle How to apply numerical tools to study dynamical systems : The CP problem
Aranda May, Montserrat
Numerical analysis
Numerical Methods
Dynamical Systems
Hamiltonian Systems
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65P Numerical problems in dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
title_short How to apply numerical tools to study dynamical systems : The CP problem
title_full How to apply numerical tools to study dynamical systems : The CP problem
title_fullStr How to apply numerical tools to study dynamical systems : The CP problem
title_full_unstemmed How to apply numerical tools to study dynamical systems : The CP problem
title_sort How to apply numerical tools to study dynamical systems : The CP problem
dc.creator.none.fl_str_mv Aranda May, Montserrat
author Aranda May, Montserrat
author_facet Aranda May, Montserrat
author_role author
dc.contributor.none.fl_str_mv Ollé Torner, Mercè
dc.subject.none.fl_str_mv Numerical analysis
Numerical Methods
Dynamical Systems
Hamiltonian Systems
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65P Numerical problems in dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
topic Numerical analysis
Numerical Methods
Dynamical Systems
Hamiltonian Systems
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65P Numerical problems in dynamical systems
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
description Given a system of differential equations, normally it is not possible to find the associated solutions analytically, so other ways have to be taken into account in order to describe the behaviour of the system. The goal of this thesis is to study how to construct numerically the skeleton of a given dynamical system, starting with the computation of the easiest solutions -equilibrium points- and following with other invariant objects as manifolds of equilibria, homoclinic orbits, periodic orbits (PO), manifolds of PO, chaos, island chains, etc. Thanks to these particular solutions and using well-known theory of Dynamical Systems, one can get an idea of the general behaviour of the system. The project studies the particular case of the system that models the behaviour of a hydrogen atom in a circularly polarized microwave field (CP problem).
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-07-01
2014
2014-10-17
dc.type.none.fl_str_mv master thesis
http://purl.org/coar/resource_type/c_bdcc
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2099.1/23113
url https://hdl.handle.net/2099.1/23113
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.publisher.none.fl_str_mv Universitat Politècnica de Catalunya
publisher.none.fl_str_mv Universitat Politècnica de Catalunya
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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