k-symplectic Lie systems: theory and applications
| Autor: | de Lucas, J., Vilariño, S. |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | J. Differential Equations 258 (6), 2221--2255 (2015) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jde.2014.12.005 |
| Popis: | A Lie system is a system of first-order ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional real Lie algebra of vector fields: a so-called Vessiot-Guldberg Lie algebra. We suggest the definition of a particular class of Lie systems, the $k$-symplectic Lie systems, admitting a Vessiot-Guldberg Lie algebra of Hamiltonian vector fields with respect to the presymplectic forms of a $k$-symplectic structure. We devise new $k$-symplectic geometric methods to study their superposition rules, time independent constants of motion and general properties. Our results are illustrated by examples of physical and mathematical interest. As a byproduct, we find a new interesting setting of application of the $k$-symplectic geometry: systems of first-order ordinary differential equations. Comment: 29 pages. An example and several minor details were corrected |
| Databáze: | arXiv |
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