Reduction and reconstruction of multisymplectic Lie systems

De Lucas, Javier ; Gràcia, Xavier ; Rivas, Xavier ; Román-Roy, Narciso ; Vilariño, Silvia (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1088/1751-8121/ac78ab

Año: 2022

Publicado en: Journal of Physics A-Mathematical and Theoretical 55, 29 (2022), 295204 [35 pp.]
ISSN: 1751-8113

Factor impacto JCR: 2.1 (2022)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 14 / 56 = 0.25 (2022) - Q1 - T1
Categ. JCR: PHYSICS, MULTIDISCIPLINARY rank: 47 / 85 = 0.553 (2022) - Q3 - T2

Factor impacto CITESCORE: 4.0 - Mathematics (Q1) - Physics and Astronomy (Q2)

Factor impacto SCIMAGO: 0.718 - Mathematical Physics (Q2) - Modeling and Simulation (Q2) - Statistics and Probability (Q2) - Statistical and Nonlinear Physics (Q2) - Physics and Astronomy (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E48-20R
Financiación: info:eu-repo/grantAgreement/ES/MCIU/RED2018-102541-T
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PGC2018-098265-B-C31
Financiación: info:eu-repo/grantAgreement/ES/MICIU/PGC2018-098265-B-C33

Tipo y forma: Article (Published version)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)