{"id":{"repo_id":"burgos","oai_identifier":"oai:riubu.ubu.es:10259/106"},"canonical_url":"https://search.dev.ndltd.org/etd/burgos/oai:riubu.ubu.es:10259/106","repository":{"repo_id":"burgos","name":"Universidad de Burgos","base_url":"https://riubu.ubu.es/oai/request"},"display":{"title":"Integrabilidad de sistemas no lineales hamiltonianos con N grados de libertad","abstract":"Esta Tesis presenta nuevos sistemas hamiltonianos clásicos completamente integrables N dimensionales, construidos mediante la técnica de simetría de coálgebra. Primeramente se ha obtenido la condición necesaria de integrabilidad para una representación simpléctica de cualquier coálgebra de Poisson. Esta condición ha sido utilizada sistemáticamente para describir los sistemas integrables de álgebras de dimensión 3, 4, 5 y 6. En segundo lugar, se ha utilizado el álgebra “two-photon” para introducir nuevas familias de sistemas N dimensionales cuasi-integrables, incluyendo, sistemas naturales, flujos geodésicos y hamiltonianos electromagnéticos, demostrando la integrabilidad de algunos de ellos mediante diferentes técnicas algebraicas. Como ejemplo representativo, se han introducido dos familias de perturbaciones ND integrables para el oscilador armónico. Finalmente, dentro del enfoque de la simetría de coálgebra, presentamos las generalizaciones N dimensionales de sistemas integrables bidimensionales. En particular, se han introducido nuevas generalizaciones de los sistemas de Hénon-Heiles, los potenciales de Ramani y osciladores cuárticos acoplados. __________________ This Ph.D. Thesis presents the construction of new completely integrable classical Hamiltonian systems with N degrees of freedom through the coalgebra symmetry approach. Firstly, we have obtained the necessary integrability condition for a symplectic realization of any Poisson coalgebra, which has been systematically explored for dimensions 3,4,5 and 6. The associated integrable systems have been fully described. Secondly, the ¨two-photon¨ algebra has been used to introduce many new families of quasi-integrable Hamiltonians in N dimensions, including natural systems, geodesic flows and electromagnetic Hamiltonians. Some of them have been shown to be completely integrable through different algebraic techniques. As outstanding examples, two new families of nonlinear perturbations of the N-dimensional harmonic oscillator have been introduced. Finally, N dimensional generalizations of two-dimensional integrable systems have been presented by making use of the coalgebra approch. In particular, new generalized Hénon-Heiles systems, Ramani potentials and coupled ND quartic oscillators have been constructed.","abstract_html":"Esta Tesis presenta nuevos sistemas hamiltonianos clásicos completamente integrables N dimensionales, construidos mediante la técnica de simetría de coálgebra. Primeramente se ha obtenido la condición necesaria de integrabilidad para una representación simpléctica de cualquier coálgebra de Poisson. Esta condición ha sido utilizada sistemáticamente para describir los sistemas integrables de álgebras de dimensión 3, 4, 5 y 6. En segundo lugar, se ha utilizado el álgebra “two-photon” para introducir nuevas familias de sistemas N dimensionales cuasi-integrables, incluyendo, sistemas naturales, flujos geodésicos y hamiltonianos electromagnéticos, demostrando la integrabilidad de algunos de ellos mediante diferentes técnicas algebraicas. Como ejemplo representativo, se han introducido dos familias de perturbaciones ND integrables para el oscilador armónico. Finalmente, dentro del enfoque de la simetría de coálgebra, presentamos las generalizaciones N dimensionales de sistemas integrables bidimensionales. En particular, se han introducido nuevas generalizaciones de los sistemas de Hénon-Heiles, los potenciales de Ramani y osciladores cuárticos acoplados. __________________ This Ph.D. Thesis presents the construction of new completely integrable classical Hamiltonian systems with N degrees of freedom through the coalgebra symmetry approach. Firstly, we have obtained the necessary integrability condition for a symplectic realization of any Poisson coalgebra, which has been systematically explored for dimensions 3,4,5 and 6. The associated integrable systems have been fully described. Secondly, the ¨two-photon¨ algebra has been used to introduce many new families of quasi-integrable Hamiltonians in N dimensions, including natural systems, geodesic flows and electromagnetic Hamiltonians. Some of them have been shown to be completely integrable through different algebraic techniques. As outstanding examples, two new families of nonlinear perturbations of the N-dimensional harmonic oscillator have been introduced. Finally, N dimensional generalizations of two-dimensional integrable systems have been presented by making use of the coalgebra approch. In particular, new generalized Hénon-Heiles systems, Ramani potentials and coupled ND quartic oscillators have been constructed.","abstract_has_math":false,"creators":["Blasco Sanz, Alfonso"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Ballesteros Castañeda, Ángel"],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-24T01:26:43Z","subjects":["Sistemas hamiltonianos","integrabilidad","coálgebras","N-dimensionales","osciladores no lineales","Hamiltonian systems","integrability","coalgebras","N-dimensional","nonlinear"],"languages":["spa","eng"],"rights":["Attribution-NonCommercial-NoDerivs 3.0 Unported"],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/3.0/es/"],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.36443/10259/106"],"render_values":[{"text":"10.36443/10259/106","href":"https://doi.org/10.36443/10259/106","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10259/106","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Ballesteros Castañeda, Ángel"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Universidad de Burgos. Departamento de Física"]},{"key":"dc:creator","label":"Author","values":["Blasco Sanz, Alfonso"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2010-06-24T10:46:29Z","2014-07-28T16:03:16Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2010-06-24T10:46:29Z","2014-07-28T16:03:16Z"]},{"key":"dc:date.issued","label":"Date","values":["2009"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Sistemas hamiltonianos","integrabilidad","coálgebras","N-dimensionales","osciladores no lineales","Hamiltonian systems","integrability","coalgebras","N-dimensional","nonlinear"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["spa","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Attribution-NonCommercial-NoDerivs 3.0 Unported"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-nd/3.0/es/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.36443/10259/106"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10259/106"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Esta Tesis presenta nuevos sistemas hamiltonianos clásicos completamente integrables N dimensionales, construidos mediante la técnica de simetría de coálgebra. Primeramente se ha obtenido la condición necesaria de integrabilidad para una representación simpléctica de cualquier coálgebra de Poisson. Esta condición ha sido utilizada sistemáticamente para describir los sistemas integrables de álgebras de dimensión 3, 4, 5 y 6. En segundo lugar, se ha utilizado el álgebra “two-photon” para introducir nuevas familias de sistemas N dimensionales cuasi-integrables, incluyendo, sistemas naturales, flujos geodésicos y hamiltonianos electromagnéticos, demostrando la integrabilidad de algunos de ellos mediante diferentes técnicas algebraicas. Como ejemplo representativo, se han introducido dos familias de perturbaciones ND integrables para el oscilador armónico. Finalmente, dentro del enfoque de la simetría de coálgebra, presentamos las generalizaciones N dimensionales de sistemas integrables bidimensionales. En particular, se han introducido nuevas generalizaciones de los sistemas de Hénon-Heiles, los potenciales de Ramani y osciladores cuárticos acoplados. __________________ This Ph.D. Thesis presents the construction of new completely integrable classical Hamiltonian systems with N degrees of freedom through the coalgebra symmetry approach. Firstly, we have obtained the necessary integrability condition for a symplectic realization of any Poisson coalgebra, which has been systematically explored for dimensions 3,4,5 and 6. The associated integrable systems have been fully described. Secondly, the ¨two-photon¨ algebra has been used to introduce many new families of quasi-integrable Hamiltonians in N dimensions, including natural systems, geodesic flows and electromagnetic Hamiltonians. Some of them have been shown to be completely integrable through different algebraic techniques. As outstanding examples, two new families of nonlinear perturbations of the N-dimensional harmonic oscillator have been introduced. Finally, N dimensional generalizations of two-dimensional integrable systems have been presented by making use of the coalgebra approch. In particular, new generalized Hénon-Heiles systems, Ramani potentials and coupled ND quartic oscillators have been constructed."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Integrabilidad de sistemas no lineales hamiltonianos con N grados de libertad"]}]}],"canonical_facts":{"dc:contributor.advisor":["Ballesteros Castañeda, Ángel"],"dc:contributor.other":["Universidad de Burgos. Departamento de Física"],"dc:creator":["Blasco Sanz, Alfonso"],"dc:date.accessioned":["2010-06-24T10:46:29Z","2014-07-28T16:03:16Z"],"dc:date.available":["2010-06-24T10:46:29Z","2014-07-28T16:03:16Z"],"dc:date.issued":["2009"],"dc:description.abstract":["Esta Tesis presenta nuevos sistemas hamiltonianos clásicos completamente integrables N dimensionales, construidos mediante la técnica de simetría de coálgebra. Primeramente se ha obtenido la condición necesaria de integrabilidad para una representación simpléctica de cualquier coálgebra de Poisson. Esta condición ha sido utilizada sistemáticamente para describir los sistemas integrables de álgebras de dimensión 3, 4, 5 y 6. En segundo lugar, se ha utilizado el álgebra “two-photon” para introducir nuevas familias de sistemas N dimensionales cuasi-integrables, incluyendo, sistemas naturales, flujos geodésicos y hamiltonianos electromagnéticos, demostrando la integrabilidad de algunos de ellos mediante diferentes técnicas algebraicas. Como ejemplo representativo, se han introducido dos familias de perturbaciones ND integrables para el oscilador armónico. Finalmente, dentro del enfoque de la simetría de coálgebra, presentamos las generalizaciones N dimensionales de sistemas integrables bidimensionales. En particular, se han introducido nuevas generalizaciones de los sistemas de Hénon-Heiles, los potenciales de Ramani y osciladores cuárticos acoplados. __________________ This Ph.D. Thesis presents the construction of new completely integrable classical Hamiltonian systems with N degrees of freedom through the coalgebra symmetry approach. Firstly, we have obtained the necessary integrability condition for a symplectic realization of any Poisson coalgebra, which has been systematically explored for dimensions 3,4,5 and 6. The associated integrable systems have been fully described. Secondly, the ¨two-photon¨ algebra has been used to introduce many new families of quasi-integrable Hamiltonians in N dimensions, including natural systems, geodesic flows and electromagnetic Hamiltonians. Some of them have been shown to be completely integrable through different algebraic techniques. As outstanding examples, two new families of nonlinear perturbations of the N-dimensional harmonic oscillator have been introduced. Finally, N dimensional generalizations of two-dimensional integrable systems have been presented by making use of the coalgebra approch. In particular, new generalized Hénon-Heiles systems, Ramani potentials and coupled ND quartic oscillators have been constructed."],"dc:format.mimetype":["application/pdf"],"dc:identifier.doi":["10.36443/10259/106"],"dc:identifier.uri":["http://hdl.handle.net/10259/106"],"dc:language.iso":["spa","eng"],"dc:rights":["Attribution-NonCommercial-NoDerivs 3.0 Unported"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-nd/3.0/es/"],"dc:subject":["Sistemas hamiltonianos","integrabilidad","coálgebras","N-dimensionales","osciladores no lineales","Hamiltonian systems","integrability","coalgebras","N-dimensional","nonlinear"],"dc:title":["Integrabilidad de sistemas no lineales hamiltonianos con N grados de libertad"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T01:26:43Z"}