Stratified lie systems: theory and applications

Cariñena, J F (Universidad de Zaragoza) ; de Lucas, J ; Wysocki, D

Resumen: A stratified Lie system is a nonautonomous system of first-order ordinary differential equations on a manifold M described by a t-dependent vector field $X={\sum }_{\alpha =1}^{r}{g}_{\alpha }{X}_{\alpha }$, where X1, ..., Xr are vector fields on M spanning an r-dimensional Lie algebra that are tangent to the strata of a stratification $\mathcal{F}$ of M while ${g}_{1},\dots ,{g}_{r}:\mathbb{R}\times M\to \mathbb{R}$ are functions depending on t that are constant along integral curves of X1, ..., Xr for each fixed t. We analyse the particular solutions of stratified Lie systems and how their properties can be obtained as generalisations of those of Lie systems. We illustrate our results by studying Lax pairs and a class of t-dependent Hamiltonian systems. We study stratified Lie systems with compatible geometric structures. In particular, a class of stratified Lie systems on Lie algebras are studied via Poisson structures induced by r-matrices.

Idioma: Inglés

DOI: 10.1088/1751-8121/ac89bd

Año: 2022

Publicado en: Journal of Physics A-Mathematical and Theoretical 55, 38 (2022), 385206 [31 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/MINECO/PGC2018-098265-B-C31

Tipo y forma: Article (Published version)

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