Some tastings in Morales-Ramis theory
In this paper we present a short material concerning to some results in Morales-Ramis theory, which relates two different notions of integrability: Integrability of Hamiltonian systems through Liouville Arnold theorem and integrability of linear differential equations through differential Galois the...
- Autores:
-
Acosta Humánez, P.
Jiménez, G.
- Tipo de recurso:
- Fecha de publicación:
- 2019
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- eng
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/4487
- Acceso en línea:
- https://hdl.handle.net/20.500.12442/4487
- Palabra clave:
- Rights
- License
- Attribution-NonCommercial-NoDerivatives 4.0 Internacional
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Some tastings in Morales-Ramis theory |
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Some tastings in Morales-Ramis theory |
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Some tastings in Morales-Ramis theory |
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Some tastings in Morales-Ramis theory |
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Some tastings in Morales-Ramis theory |
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Some tastings in Morales-Ramis theory |
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Some tastings in Morales-Ramis theory |
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Acosta Humánez, P. Jiménez, G. |
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Acosta Humánez, P. Jiménez, G. |
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In this paper we present a short material concerning to some results in Morales-Ramis theory, which relates two different notions of integrability: Integrability of Hamiltonian systems through Liouville Arnold theorem and integrability of linear differential equations through differential Galois theory. As contribution, we obtain the abelian differential Galois group of the variational equation related to a bi-parametric Hamiltonian system. |
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2019 |
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2019-12-17T20:05:44Z |
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2019-12-17T20:05:44Z |
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2019 |
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article |
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http://purl.org/coar/resource_type/c_6501 |
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17426588 |
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https://hdl.handle.net/20.500.12442/4487 |
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eng |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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IOP Publishing |
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Journal of Physics: Conference Series Vol. 1414 No. 1 (2019). 5th International Week of Science, Technology & Innovation |
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10.1088/1742-6596/1414/1/012011 |
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Acosta Humánez, P.699ad3c6-acf4-4df8-ab0f-eaac1ce5f402Jiménez, G.0860f4c5-5bcd-4b94-b498-cd9d4f9486d22019-12-17T20:05:44Z2019-12-17T20:05:44Z201917426588https://hdl.handle.net/20.500.12442/4487In this paper we present a short material concerning to some results in Morales-Ramis theory, which relates two different notions of integrability: Integrability of Hamiltonian systems through Liouville Arnold theorem and integrability of linear differential equations through differential Galois theory. As contribution, we obtain the abelian differential Galois group of the variational equation related to a bi-parametric Hamiltonian system.engIOP PublishingAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/http://purl.org/coar/access_right/c_abf2Journal of Physics: Conference SeriesVol. 1414 No. 1 (2019). 5th International Week of Science, Technology & Innovation10.1088/1742-6596/1414/1/012011Some tastings in Morales-Ramis theoryarticlehttp://purl.org/coar/resource_type/c_6501Acosta-Humánez P and Blazquez-Sanz D 2008 Non integrability of some hamiltonians with rational potentials Discrete and Continuous Dynamical Systems-B 10(2) 265Acosta-Humánez P 2009 Nonautonomous hamiltonian systems and Morales-Ramis Theory 1. The case ̈=f (x, t) SIAM Journal on Applied Dynamical Systems 8(1) 279Acosta-Humánez P, Morales-Ruiz J and Weil J A 2011 Galoisian approach to integrability of Schrödinger equation Reports on Mathematical Physics 67(3) 350Acosta-Humánez P, Alvarez-Ramírez M, and Delgado J 2009 Non-integrability of some few body problems in two degrees of freedom Qualitative Theory of Dynamical System 8(2) 209Arnold V 2013 Mathematical methods of classical mechanics (Luxemburgo: Springer Science & Business Media)Audin M 2001 Les systems hamiltoniens et leur intégrabilité, cours Spécialisés (France: Société mathématique de France et EDP Sciences)Morales-Ruiz J and Ramis J P 2001 Galoisian obstructions to integrability of hamiltonians systems I Methods and Applications of Analysis 8(1) 33Morales-Ruiz J 1999 Differential galois theory and non integrability of hamiltonians systems (Basilea: Birkhäuser Basel)Acosta-Humánez P, Lázaro Ochoa J, Morales-Ruiz J, and Pantazi C 2015 On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory Discrete and Continuous Dynamical Systems- A 35(5) 1767Acosta-Humánez P 2010 Galoisian approach to supersymmetric quantum mechanics: The integrability analysis the Schrödinger equation by means of differential Galois theory (Saarbrucken: VDM Publishing)Morales-Ruiz J and Ramis J P 2001 Galoisian obstructions to integrability of Hamiltonians systems II Methods and Applications of Analysis 8(1) 97Morales-Ruiz J, Ramis J P and Simó C 2007 Integrability of Hamiltonians systems and differential Galois group of higher variational equations Annales Scitifiques de l’Ecole Normale Supérieure 40(6) 845Acosta Humánez P 2006 La teoría de Morales-Ramis y el algoritmo de Kovacic Lecturas Matemáticas 2 21ORIGINALPDF.pdfPDF.pdfPDFapplication/pdf519989https://bonga.unisimon.edu.co/bitstreams/b6bbdbf5-e305-4f55-b1f7-0b5c69f8540a/downloadad03870401dfbc3b1aabc9b631b97079MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://bonga.unisimon.edu.co/bitstreams/d917e827-e479-4383-8215-2ced68fcb28e/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-8381https://bonga.unisimon.edu.co/bitstreams/6a3495b0-cb3d-40d0-bef0-e1837dfc6eaa/download733bec43a0bf5ade4d97db708e29b185MD53TEXTSometastingsinMoralesRamistheory.pdf.txtSometastingsinMoralesRamistheory.pdf.txtExtracted texttext/plain16721https://bonga.unisimon.edu.co/bitstreams/05b87f39-d9e0-4a45-8b2f-42f666f121fb/downloade0347f04114298d108457a609039ee3aMD54PDF.pdf.txtPDF.pdf.txtExtracted texttext/plain17365https://bonga.unisimon.edu.co/bitstreams/fdd85977-280c-4c10-a832-b69b26c3e646/downloadb1279fc1d3983fc76bab8acdd3721040MD56THUMBNAILSometastingsinMoralesRamistheory.pdf.jpgSometastingsinMoralesRamistheory.pdf.jpgGenerated Thumbnailimage/jpeg1282https://bonga.unisimon.edu.co/bitstreams/c3b24523-2dbb-432d-a2ba-1295be71f5d9/download9022109f58e99bf4e456f796cf00c855MD55PDF.pdf.jpgPDF.pdf.jpgGenerated Thumbnailimage/jpeg3175https://bonga.unisimon.edu.co/bitstreams/99be6d41-a821-4cf4-9fc8-b909b9dbd216/download3ae78b7f6d0c7f375fac1903354156dfMD5720.500.12442/4487oai:bonga.unisimon.edu.co:20.500.12442/44872024-08-14 21:52:36.031http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internacionalopen.accesshttps://bonga.unisimon.edu.coRepositorio Digital Universidad Simón Bolívarrepositorio.digital@unisimon.edu.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 |