Reduction and reconstruction of multisymplectic Lie systems
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie algebra of vector fields, a so-called Vessiot–Guldberg Lie algebra. In this work, multisymplectic form...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| 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:2117/373745 |
| Acceso en línea: | https://hdl.handle.net/2117/373745 https://dx.doi.org/10.1088/1751-8121/ac78ab |
| Access Level: | acceso abierto |
| Palabra clave: | Lie algebras Lie system Multisymplectic manifold Multisymplectic reduction and reconstruction Vessiot–Guldberg Lie algebra Lie group Time-dependent harmonic oscillator Energy–momentum method Lie, Àlgebres de Classificació AMS::17 Nonassociative rings and algebras::17B Lie algebras and Lie superalgebras Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Anells i àlgebres |
| Sumario: | A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie algebra of vector fields, a so-called Vessiot–Guldberg Lie algebra. In this work, multisymplectic forms are applied to the study of the reduction of Lie systems through their Lie symmetries. By using a momentum map, we perform a reduction and reconstruction procedure of multisymplectic Lie systems, which allows us to solve the original problem by analysing several simpler multisymplectic Lie systems. Conversely, we study how reduced multisymplectic Lie systems allow us to retrieve the form of the multisymplectic Lie system that gave rise to them. Our results are illustrated with examples from physics, mathematics, and control theory. |
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