k-Symplectic Lie systems: theory and applications

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

de Lucas, J.¹  Vilarino, S.^2,3 

[1] Univ Warsaw, Dept Math Methods Phys, PL-02093 Warsaw, Poland

[2] Ctr Univ Def Zaragoza, E-50090 Zaragoza, Spain

[3] IUMA, E-50090 Zaragoza, Spain

关键词: k-Symplectic structure;    Lie system;    Poisson structure;    Superposition rule;    Vessiot-Guldberg Lie algebra;   

DOI  :  10.1016/j.jde.2014.12.005

来源: Elsevier

【 摘 要 】

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, t-independent constants of motion and general properties. Our results are illustrated through 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free